Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61106 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C29 |
| direct product | C11×#61107 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C2×D42 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
2624 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 5 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,23)(15,20)(16,32)(17,21)(18,26)(19,30)(22,33)(24,41)(25,40)(27,35)(28,36)(29,37)(31,38)(34,43)(39,42);(12,14,17,28)(13,18,21,35)(15,24,31,43)(16,27,33,26)(19,34,37,41)(20,39,38,40)(22,36,32,23)(25,30,42,29);(12,15)(13,19)(14,24)(16,29)(17,31)(18,34)(20,32)(21,37)(22,38)(23,39)(25,27)(26,42)(28,43)(30,33)(35,41)(36,40);(12,15)(13,20)(14,25)(16,30)(17,31)(18,34)(19,32)(21,38)(22,37)(23,40)(24,27)(26,43)(28,42)(29,33)(35,41)(36,39);(13,21)(18,35)(19,37)(20,38)(22,32)(23,36)(34,41)(39,40)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54095);