Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9109 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#10974 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #386 |
| commutator | C24 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1258 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(16,17,20,25,21,24,33,39)(18,26,28,40,29,22,32,35)(19,23,31,38,30,37,43,47)(27,36,42,46,41,34,44,45);(16,18,21,29)(17,22,24,26)(19,27,30,41)(20,32,33,28)(23,36,37,34)(25,40,39,35)(31,44,43,42)(38,45,47,46);(13,15)(16,19)(17,23)(18,27)(20,31)(21,30)(22,34)(24,37)(25,38)(26,36)(28,42)(29,41)(32,44)(33,43)(35,45)(39,47)(40,46)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3962);