Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #534 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C11 · Schur multiplier (H2) = C23×C4 |
| direct product | C11×#17329 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C11 | C24 |
| commutator | C22 | C22×C42×C11 |
| Frattini, cosocle | C42 | C24×C11 |
| socle | C22×C11 | C22×C42 |
| prime radical | C2×C11×#41 | C2×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C42×C11 ◁ G | |
718 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,19,16,17,22,24)(14,18,21,25,20,23,26,27)(28,29)(30,33)(31,35)(32,34)(36,40)(37,39)(38,41)(42,43);(13,17)(18,23)(19,24)(25,27)(28,30,31,36,32,37,38,42)(29,33,35,40,34,39,41,43);(12,14)(13,18)(15,21)(16,20)(17,23)(19,25)(22,26)(24,27)(29,34)(33,39)(35,41)(40,43);(14,20)(18,23)(21,26)(25,27)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 10317);