Finite Group DatabasebetaFinite Group Databasebeta| order | 43008 |
| isoclinism | isoclinic class of #72227690 |
| automorphism | ? |
| homology | Abelianization (H1) = C1 · Schur multiplier (H2) = C1 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #72209649 |
| commutator, hypocenter | G | C1 |
| Frattini, socle | C25 | AGL(3,𝔽2) |
| Fitting, cosocle | C22×C43 | GL(3,𝔽2) |
| LCS | G | |
| UCS | C1 ◁ C22 | |
1379 conjugacy classes of subgroups; only the 13 normal subgroups are shown.
This group has 1379 conjugacy classes of subgroups — too many to draw. Only its 13 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 60 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 2 generators on 60 points:
(1,10,4,9,14,13)(2,11,8,5,16,6)(3,15)(7,12)(17,24,32,23,25,28)(18,30,20,21,26,19)(22,31)(27,29)(33,58,57,43,54,50,37,59,55,36,60,56)(34,48,53,38,41,51)(35,45,44,42,52,39)(40,49,47,46);(2,3,7)(8,11,10)(9,12,15)(13,14,16)(18,23,25)(20,21,24)(26,31,32)(28,29,30)(33,35,40)(36,41,49)(37,42,47)(43,48,46)(45,50,54)(51,55,58)(52,56,60)(53,57,59)56 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,10,4,9,14,13)(2,11,8,5,16,6)(3,15)(7,12)(17,24,32,23,25,28)(18,30,20,21,26,19)(22,31)(27,29)(33,58,57,43,54,50,37,59,55,36,60,56)(34,48,53,38,41,51)(35,45,44,42,52,39)(40,49,47,46), (2,3,7)(8,11,10)(9,12,15)(13,14,16)(18,23,25)(20,21,24)(26,31,32)(28,29,30)(33,35,40)(36,41,49)(37,42,47)(43,48,46)(45,50,54)(51,55,58)(52,56,60)(53,57,59));