Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61049 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#61491 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#529 ◁ G | |
1770 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,16)(17,19)(20,21,25,29)(22,26,31,41)(23,33,36,45)(24,37,39,28)(27,38,44,35)(30,46,34,51)(32,49,48,42)(40,50,43,47);(12,13)(14,17)(15,16)(18,19)(20,22)(21,26)(23,34)(24,32)(25,31)(27,43)(28,42)(29,41)(30,36)(33,51)(35,50)(37,49)(38,47)(39,48)(40,44)(45,46);(20,23,25,36)(21,27,29,44)(22,30,31,34)(24,38,39,35)(26,40,41,43)(28,45,37,33)(32,50,48,47)(42,51,49,46);(13,16)(17,19);(12,14,15,18)(13,17,16,19)(22,31)(26,41)(30,34)(32,48)(40,43)(42,49)(46,51)(47,50)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54479);