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×#33721 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C2×C11×#508 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#117 ◁ C11×#405 ◁ G | |
794 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 79 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(16,17,22,27)(18,28,33,53)(19,24,34,45)(20,37,39,65)(21,40,38,26)(23,41,44,31)(25,48,49,29)(30,50,56,72)(32,60,59,52)(35,63,61,78)(36,64,62,47)(42,66,68,57)(43,54,51,67)(46,71,70,55)(58,77,76,74)(69,75,73,79);(16,18,29,54,21,32,39,41,22,33,48,67,38,59,20,31)(17,23,37,52,26,43,49,53,27,44,65,60,40,51,25,28)(19,30,55,75,36,58,61,66,34,56,71,79,62,76,35,57)(24,42,63,74,47,69,70,72,45,68,78,77,64,73,46,50);(12,13,14,15)(16,19)(17,24)(18,30)(20,35)(21,36)(22,34)(23,42)(25,46)(26,47)(27,45)(28,50)(29,55)(31,57)(32,58)(33,56)(37,63)(38,62)(39,61)(40,64)(41,66)(43,69)(44,68)(48,71)(49,70)(51,73)(52,74)(53,72)(54,75)(59,76)(60,77)(65,78)(67,79);(19,34)(24,45)(30,56)(35,61)(36,62)(42,68)(46,70)(47,64)(50,72)(55,71)(57,66)(58,76)(63,78)(69,73)(74,77)(75,79)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26709);