|
group | subgroup | status | comment | action
|
|
| 2G2(q) | 2× L(2,q) | not
MF | proof in paper; char table, Ward... | |
|
3D4(q) | G2(q) | not MF | in Ross
Lawther notes | JS |
|
3D4(q)
| 3D4(q1/2) | not MF | by Lawther,
Durham Proc LMS | |
|
3D4(q) | N(A1(q)·
A1(q3))) | not MF | our orbits on hex
argument | ML |
|
3D4(2) | 72 2Alt4 | no dtg | not mf(?)
arg on paper | finite |
|
3D4(2) | 31+22Sym4 | no dtg | not mf(?), arg on paper | finite |
|
3D4(2) | (7× L3(2))2 | no
dtg?
| not mf(?) | finite |
|
G2(q) | SL3eps(q)2 | is MF but
no dtg | MF by LPS 2
closures; no dtg by 2-closure | JS |
|
G2(q) | G2(q1/2) | not MF if p
!= 3; MF if p=3 with graph auto | see [Lp]
for subdegrees | AMC |
|
G2(q) | 2G2(q) | p=3, MF | see
Lawther G2 LMS proc, need to investigate dtg | AMC |
|
G2(q) | N(A1(q)·
A1(q))) | no dtg | hex argument | JS |
|
G2(4) | J2 | rank 3 | see Atlas, Suz
tower | finite |
|
G2(q).graph
| Borel.graph | is
Gen 12-gon of order (q,1) | p=3 | |
|
2F4(2)' | L(2,25) | MF but no dtg |
char has non-real
constituents (also with auto?) | finite |
|
2F4(2)' | L(3,3)2 | no dtg | subdegrees possibilities
computed | finite |
|
2F4(2)'
| Alt62 | not MF |
by inner product computations | finite |
|
2F4(2)' | 52 4 Alt4 |
? | see Atlas? | finite |
|
F4(q) | B4(q) | MF but no dtg | Ross
L.,
see paper in J.
Algebra | AMC |
|
F4(q) | D4(q). Sym3 | not MF
except for q=2 | Ross Lawther: to be written up | RL |
|
F4(2) | D4(2). Sym3 | ? | ? | finite |
|
F4(q) | 3D4(q).3 | not
MF | Ross Lawther: to be written up | RL |
|
F4(q) | F4(q1/2) |
not MF | Ross Lawther: [Ld] | |
|
F4(q) | 2F4(q) | not MF |
q=2*,. Proof by Ross Lawther in [Ld] |
|
F4(2) | L4(3)2 | ? | have GAP
character | finite |
|
F4(q).graph
| parab A1(q)A1(q).graph | not
MF | q even; see Lawther Sep 2002 | |
|
F4(q).graph
| parab B2(q).graph | not
MF | q even; see Lawther Sep 2002 | |
|
E6eps(q)
| N(A1(q)A5eps(q)) | ? | q
odd:~involution centralizer | ML |
|
E6eps(q)
| N(A1(q)A5eps(q)) | not MF | Ivanov
argument | ML |
|
E6eps(q)
| N(D5eps(q))=D5eps(q)T1eps | not
DTG? | torus
contains centre of E6; van Bon's kernel chain | JS |
|
E6(q)
| E6delta(q1/2) | not
MF | see [Ld] | AMC |
|
E6eps(q) | F4(q) | MF |
see [Lb], with subdegrees given
on pp. 134 and 143 | AMC |
|
E6eps(q) | C4(q) | no dtg | q odd by
max. subgp cond;
see invol arg on paper | ML |
|
E6-(2)
| Fi22 | no dtg? | have page from Norton
with subdegrees; there is Saxl arg for
unimodality | JS |
|
E6(q).graph
| parab A5(q).graph | not
MF | see Lawther Sep 2002 | |
|
E6(q).graph
| parab D4(q).graph | not
MF | see Lawther Sep 2002 | |
|
E6(q).graph
| parab A2(q)A1(q)A1(q).graph | not
MF | see Lawther Sep 2002 | |
| E7(q) | N(E6eps(q)) =
E6epsTeps1 | ? | if q
is odd, the involution centralizer trick works; try van Bon's kernel
chain | ML |
|
E7(q)
| E6epsTeps12 | q
even: Y trick gives q = 2, 4 | ML |
|
E7(q) | N(A1(q)D6(q)) | not MF
by orbit arg paper 87 | ML |
|
E7(q) | E7(q1/2) | not MF
| [Ld] | |
|
E7(q) | N(A7(q))=A7(q)2 |
not MF | by orbits on roots arg 1987 | ML |
|
E7(q) | N(A7-(q2))=A7-(q2) | ? | if
q odd, the involution centralizer trick works | ML |
|
E7(q) | A7-(q2) | ?
| q
even: Y=C4 trick works for q not 2 or 4;spherical so get finite mults on
unipot char | ML |
|
E7(q)
| A7-(q2) | ? | q=2,4 | finite |
|
E8(q) | N(D8(q)) | not MF | by root study 1987
| JS |
|
E8(q) | N(A1(q)E7(q)) | not MF | by
Section e8ona1e7 | JS |
|
E8(q) | E8(q1/2) | not MF | [Ld] | |
|