Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18284 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18290 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1034 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,18)(14,22)(15,25)(19,31)(20,29)(21,26)(23,37)(24,36)(27,40)(30,32)(33,43)(34,41)(35,39)(38,42);(12,13)(14,19)(15,26)(16,21)(17,20)(18,25)(22,32)(23,38)(24,33)(27,41)(28,34)(29,40)(30,39)(31,37)(35,43)(36,42);(15,27)(18,29)(23,35)(25,40)(26,41)(30,31)(37,39)(38,43);(12,14,16,24)(13,19,21,33)(15,23,25,39)(17,22,28,36)(18,30,26,38)(20,32,34,42)(27,35,40,37)(29,31,41,43)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11278);