Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18992 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#19013 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C11×#3531 | 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)(28,29,34,37)(30,40,43,52)(31,44,46,53)(32,39,33,38)(35,47,50,42)(36,48,51,45)(41,49,57,59)(54,55,58,56);(12,13)(14,18)(15,19)(16,24)(17,20)(21,25)(22,26)(23,27)(28,30,34,43)(29,35,37,50)(31,41,46,57)(32,47,33,42)(36,49,51,59)(38,52,39,40)(44,58,53,54)(45,56,48,55);(12,14)(13,18)(15,22)(16,25)(17,23)(19,26)(20,27)(21,24)(28,31)(29,36)(30,41)(32,45)(33,48)(34,46)(35,49)(37,51)(38,44)(39,53)(40,54)(42,55)(43,57)(47,56)(50,59)(52,58);(12,15,17,16)(13,19,20,24)(14,22,23,25)(18,26,27,21)(29,37)(35,50)(36,51)(38,39)(40,52)(44,53)(49,59)(54,58)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 12001);