Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18930 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18969 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C11×#3547 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
874 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)(14,22)(15,20)(16,19)(17,21)(18,24)(23,27)(25,26)(28,29,33,37)(30,38,41,51)(31,35,42,49)(32,44,46,36)(34,45,48,40)(39,52,53,59)(43,56,55,50)(47,57,58,54);(12,14,17,25)(13,18,21,27)(15,23,16,24)(19,26,20,22)(28,30,33,41)(29,34,37,48)(31,39,42,53)(32,45,46,40)(35,47,49,58)(36,51,44,38)(43,57,55,54)(50,59,56,52);(13,19)(15,16)(18,26)(20,21)(22,27)(23,24)(28,31)(29,35)(30,39)(32,43)(33,42)(34,47)(36,50)(37,49)(38,52)(40,54)(41,53)(44,56)(45,57)(46,55)(48,58)(51,59);(12,15,17,16)(13,19,21,20)(14,23,25,24)(18,26,27,22)(31,42)(35,49)(39,53)(43,55)(47,58)(50,56)(52,59)(54,57)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11957);