Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33522 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#33585 |
| 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 | |
748 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)(16,17)(18,22)(19,23)(20,33)(21,26)(24,30)(25,31)(27,35)(28,34)(29,43)(32,39)(36,42)(37,41)(38,44)(40,45)(46,47);(12,13,14,15)(16,18)(17,22)(19,28)(20,29)(21,27)(23,34)(24,36)(25,37)(26,35)(30,42)(31,41)(32,40)(33,43)(38,46)(39,45)(44,47);(17,23)(19,30)(20,31)(22,34)(24,25)(26,39)(28,42)(29,41)(32,44)(33,38)(35,45)(36,37)(40,47)(43,46);(18,27)(22,35)(28,40)(29,41)(34,45)(36,46)(37,43)(42,47)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26573);