Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33758 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#33802 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C23×C11 | C2×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
458 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,20)(15,18)(16,19)(17,22)(21,26)(23,25)(24,27)(28,29,33,38)(30,34,39,49)(31,35,44,52)(32,45,43,37)(36,53,51,42)(40,50,54,46)(41,58,55,48)(47,56,59,57);(12,14,16,22)(13,17,19,20)(15,23,24,21)(18,26,27,25)(28,30)(29,34)(31,40)(32,41)(33,39)(35,50)(36,47)(37,48)(38,49)(42,57)(43,55)(44,54)(45,58)(46,52)(51,59)(53,56);(12,15,16,24)(13,18,19,27)(14,21,22,23)(17,25,20,26)(29,35)(30,39)(31,42)(32,43)(34,46)(36,37)(38,52)(40,56)(44,53)(45,51)(47,58)(48,59)(49,50)(54,57);(13,19)(17,20)(18,27)(25,26)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26790);