Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61609 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#62160 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#529 ◁ G | |
1648 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,19)(14,20,21,17)(15,23,24,18)(22,25,27,26)(28,29)(30,35)(31,43)(32,37)(33,46)(34,38)(36,44)(39,53)(40,49)(41,50)(42,56)(45,51)(47,52)(48,54)(55,58)(57,59);(12,14)(13,17)(15,22)(16,21)(18,25)(19,20)(23,26)(24,27)(28,30,34,41)(29,35,38,50)(31,39,45,55)(32,40,33,42)(36,48,52,59)(37,49,46,56)(43,53,51,58)(44,54,47,57);(28,31)(29,36)(30,39)(32,44)(33,47)(34,45)(35,48)(37,51)(38,52)(40,54)(41,55)(42,57)(43,46)(49,58)(50,59)(53,56);(14,21)(17,20)(22,27)(25,26)(28,32,34,33)(29,37,38,46)(30,40,41,42)(31,44,45,47)(35,49,50,56)(36,51,52,43)(39,54,55,57)(48,58,59,53);(12,15,16,24)(13,18,19,23)(14,22,21,27)(17,25,20,26)(30,41)(35,50)(39,55)(40,42)(48,59)(49,56)(53,58)(54,57)539 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 55148);