Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19086 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#19095 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C11×#3568 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
834 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11)(14,21)(15,16)(18,25)(19,23)(22,24)(26,27)(28,29,34,39)(30,40,42,52)(31,44,46,53)(32,38,33,37)(35,47,50,43)(36,48,51,45)(41,49,55,59)(54,56,58,57);(12,13)(14,18)(15,19)(16,23)(17,20)(21,26)(22,27)(24,25)(28,30)(29,35)(31,41)(32,47)(33,43)(34,42)(36,49)(37,52)(38,40)(39,50)(44,58)(45,57)(46,55)(48,56)(51,59)(53,54);(12,14)(13,18)(15,21)(16,24)(17,22)(19,26)(20,27)(23,25)(28,31)(29,36)(30,41)(32,45)(33,48)(34,46)(35,49)(37,44)(38,53)(39,51)(40,54)(42,55)(43,56)(47,57)(50,59)(52,58);(12,15,17,16)(13,19,20,23)(14,21,22,24)(18,26,27,25)(30,42)(35,50)(40,52)(41,55)(43,47)(49,59)(54,58)(56,57)341 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 12083);