Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61609 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#61923 |
| 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×#533 ◁ G | |
1696 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,22)(15,19)(16,20)(17,21)(18,24)(23,27)(25,26)(28,29,34,30)(31,39,41,43)(32,36,33,38)(35,42,37,40);(12,14,17,24)(13,18,21,22)(15,23,16,25)(19,26,20,27)(28,30,34,29)(31,37,41,35)(32,36,33,38)(39,40,43,42);(12,15,17,16)(13,19,21,20)(14,23,24,25)(18,26,22,27)(28,31)(29,35)(30,37)(32,40)(33,42)(34,41)(36,43)(38,39);(12,16,17,15)(13,20,21,19)(14,23,24,25)(18,26,22,27);(13,21)(18,22)(19,20)(26,27)(28,32,34,33)(29,36,30,38)(31,40,41,42)(35,43,37,39)539 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54911);