Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61643 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#61943 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| prime radical | C11×#535 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#533 ◁ G | |
1650 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 5 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,22)(15,19)(16,20)(17,21)(18,24)(23,27)(25,26)(28,29,34,37)(30,35,40,51)(31,42,44,53)(32,38,33,46)(36,47,52,43)(39,54,55,59)(41,49,45,50)(48,56,58,57);(12,14,17,24)(13,18,21,22)(15,23,16,25)(19,26,20,27)(28,30)(29,35)(31,39)(32,45)(33,41)(34,40)(36,48)(37,51)(38,50)(42,54)(43,57)(44,55)(46,49)(47,56)(52,58)(53,59);(12,15,17,16)(13,19,21,20)(14,23,24,25)(18,26,22,27)(28,31)(29,36)(30,39)(32,43)(33,47)(34,44)(35,48)(37,52)(38,53)(40,55)(41,56)(42,46)(45,57)(49,54)(50,59)(51,58);(12,16,17,15)(13,20,21,19)(14,23,24,25)(18,26,22,27)(29,37)(30,40)(36,52)(38,46)(39,55)(41,45)(42,53)(56,57);(13,21)(18,22)(19,20)(26,27)(28,32,34,33)(29,38,37,46)(30,41,40,45)(31,43,44,47)(35,49,51,50)(36,53,52,42)(39,56,55,57)(48,54,58,59)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54931);