Finite Group DatabasebetaFinite Group Databasebeta| order | 21504 |
| isoclinism | isoclinic class of #72209804 |
| automorphism | ? |
| homology | Abelianization (H1) = C1 · Schur multiplier (H2) = C2 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #72209649 |
| commutator, hypocenter | G | C1 |
| Frattini, socle | C24 | AGL(3,𝔽2) |
| Fitting, cosocle | C2×C43 | GL(3,𝔽2) |
| LCS | G | |
| UCS | C1 ◁ C2 | |
515 conjugacy classes of subgroups; only the 7 normal subgroups are shown.
This group has 515 conjugacy classes of subgroups — too many to draw. Only its 7 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Permutation generators:
(1,2,5,3)(4,7,6,8)(9,13,11,14)(10,15,12,16)(17,18)(19,26)(20,24)(21,25)(23,30)(27,28)(31,37)(32,36)(33,38)(39,40);(1,4,2)(3,5,6)(7,9,10)(8,11,12)(18,22,23)(24,27,32)(25,28,31)(26,29,33)(30,34,35)(36,39,42)(37,40,43)(38,41,44);(1,5)(2,3)(4,6)(7,8)(9,11)(10,12)(13,14)(15,16);(17,19)(18,24,26,25)(20,21)(23,31,33,32)(34,39,41,40)(35,42,44,43);(17,19)(18,24,26,25)(20,21)(22,27,29,28)(23,33)(30,36,38,37)(31,32)(34,41)(35,43,44,42)(39,40);(17,20,19,21)(22,29)(27,28)(30,36,38,37)(34,40,41,39)(35,43,44,42);(18,26)(23,33)(24,25)(31,32)(34,41)(35,44)(39,40)(42,43);(18,26)(22,29)(24,25)(27,28)(30,38)(35,44)(36,37)(42,43);(17,19)(20,21)(30,38)(34,41)(35,44)(36,37)(39,40)(42,43)34 conjugacy classes — view the full character table.
| maximal quotient of | #72227690 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:
gap> G := Group((1,2,5,3)(4,7,6,8)(9,13,11,14)(10,15,12,16)(17,18)(19,26)(20,24)(21,25)(23,30)(27,28)(31,37)(32,36)(33,38)(39,40), (1,4,2)(3,5,6)(7,9,10)(8,11,12)(18,22,23)(24,27,32)(25,28,31)(26,29,33)(30,34,35)(36,39,42)(37,40,43)(38,41,44), (1,5)(2,3)(4,6)(7,8)(9,11)(10,12)(13,14)(15,16), (17,19)(18,24,26,25)(20,21)(23,31,33,32)(34,39,41,40)(35,42,44,43), (17,19)(18,24,26,25)(20,21)(22,27,29,28)(23,33)(30,36,38,37)(31,32)(34,41)(35,43,44,42)(39,40), (17,20,19,21)(22,29)(27,28)(30,36,38,37)(34,40,41,39)(35,43,44,42), (18,26)(23,33)(24,25)(31,32)(34,41)(35,44)(39,40)(42,43), (18,26)(22,29)(24,25)(27,28)(30,38)(35,44)(36,37)(42,43), (17,19)(20,21)(30,38)(34,41)(35,44)(36,37)(39,40)(42,43));