Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#18434 |
| 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 ◁ C2×C42×C11 ◁ G | |
982 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)(15,26)(19,31)(20,29)(21,27)(23,35)(25,39)(28,38)(30,34)(32,42)(33,41)(36,37)(40,43);(12,13)(14,19)(15,27)(16,21)(17,20)(18,26)(22,34)(23,32)(24,33)(25,40)(28,41)(29,38)(30,37)(31,39)(35,43)(36,42);(14,23)(15,28)(18,29)(19,32)(22,35)(25,39)(26,38)(27,41)(30,42)(31,40)(34,43)(36,37);(12,14,24,35)(13,19,33,43)(15,25,38,39)(16,23,17,22)(18,30,41,42)(20,34,21,32)(26,37,28,36)(27,40,29,31)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11422);