Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18992 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#19012 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
844 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)(13,18)(15,16)(19,26)(20,23)(21,24)(25,27)(28,29)(30,37)(31,35)(32,40)(33,36)(34,38)(39,42)(41,43);(12,13,17,20)(14,19,22,27)(15,18,16,23)(21,25,24,26)(28,29)(30,34)(31,35)(32,40)(33,36)(37,41)(38,42)(39,43);(12,14)(13,19)(15,21)(16,24)(17,22)(18,25)(20,27)(23,26)(28,30)(29,34)(31,38)(32,41)(33,39)(35,42)(36,43)(37,40);(12,15,17,16)(13,18,20,23)(14,21,22,24)(19,25,27,26)(28,31,33,32)(29,35,36,40)(30,38,39,41)(34,42,43,37)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 12000);