Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19072 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#19081 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C11×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
880 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)(14,22)(15,16)(20,21)(23,24)(25,26)(28,29,34,31)(30,38,41,43)(32,37,33,36)(35,42,39,40);(12,13)(14,19)(15,20)(16,18)(17,21)(22,26)(23,25)(24,27)(28,30)(29,35)(31,39)(32,40)(33,42)(34,41)(36,38)(37,43);(12,14,17,24)(13,19,21,27)(15,22,16,23)(18,25,20,26)(28,31,34,29)(30,39,41,35)(32,36,33,37)(38,42,43,40);(12,15,17,16)(13,20,21,18)(14,23,24,22)(19,25,27,26)(28,32,34,33)(29,36,31,37)(30,40,41,42)(35,38,39,43)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 12069);