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×#33720 |
| 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 | |
858 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)(19,23)(20,30)(24,32)(25,40)(26,35)(28,36)(29,42)(31,37)(33,34)(38,43)(39,47)(41,46)(44,45);(16,17,23,34,20,25,31,35,21,26,37,40,30,33,19,22)(18,24,36,45,29,39,41,43,27,38,46,47,42,44,28,32);(12,13,14,15)(16,18)(17,24)(19,28)(20,29)(21,27)(22,32)(23,36)(25,39)(26,38)(30,42)(31,41)(33,44)(34,45)(35,43)(37,46)(40,47);(18,27)(24,38)(28,41)(29,42)(32,43)(36,46)(39,44)(45,47)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26708);