Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#33722 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#117 ◁ C11×#405 ◁ G | |
826 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(17,22)(19,30)(20,31)(23,32)(24,33)(25,37)(26,36)(28,43)(29,42)(34,35)(38,41)(39,44)(40,47)(45,46);(16,17,23,37,20,25,19,22,21,26,30,35,31,34,32,36)(18,24,38,47,29,40,28,33,27,39,43,46,42,45,41,44);(12,13,14,15)(16,18)(17,24)(19,28)(20,29)(21,27)(22,33)(23,38)(25,40)(26,39)(30,43)(31,42)(32,41)(34,45)(35,46)(36,44)(37,47);(18,27)(24,39)(28,41)(29,42)(33,44)(38,43)(40,45)(46,47)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26710);