Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8491 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#8503 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #379 |
| commutator | C42 | C22×C4×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C11×#3554 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
672 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,19,17,21,15,20)(14,22,23,18,24,26,25,27)(28,29)(30,38,41,34)(31,42,44,51)(32,37)(33,36)(35,43,49,45)(39,54)(40,53,58,48)(46,50)(47,55)(52,57)(56,59);(12,14)(13,18)(15,25)(16,23)(17,24)(19,26)(20,22)(21,27)(28,30)(29,34)(31,39)(32,40)(33,41)(35,47)(36,38)(37,48)(42,59)(43,55)(44,56)(45,57)(46,58)(49,52)(50,53)(51,54);(13,19)(15,16)(18,26)(20,21)(22,27)(23,25)(28,31,33,44)(29,35,36,49)(30,39,41,56)(32,45,46,43)(34,47,38,52)(37,51,50,42)(40,57,58,55)(48,54,53,59)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1491);