Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19050 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#19071 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C11×#3553 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
810 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)(14,21)(15,19)(16,24)(17,20)(18,22)(23,26)(25,27)(28,29,34,39)(30,40,43,52)(31,44,45,53)(32,38,33,37)(35,47,50,42)(36,48,51,46)(41,49,55,59)(54,56,58,57);(12,13)(14,18)(15,19)(16,24)(17,20)(21,25)(22,26)(23,27)(28,30)(29,35)(31,41)(32,47)(33,42)(34,43)(36,49)(37,52)(38,40)(39,50)(44,58)(45,55)(46,57)(48,56)(51,59)(53,54);(12,14)(13,18)(15,22)(16,25)(17,23)(19,26)(20,27)(21,24)(28,31,34,45)(29,36,39,51)(30,41,43,55)(32,46,33,48)(35,49,50,59)(37,44,38,53)(40,54,52,58)(42,56,47,57);(12,15,17,16)(13,19,20,24)(14,22,23,25)(18,26,27,21)(31,45)(36,51)(41,55)(44,53)(46,48)(49,59)(54,58)(56,57)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 12059);