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×#61922 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| prime radical | C11×#449 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#533 ◁ G | |
1640 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)(14,22)(15,19)(16,20)(17,21)(18,24)(23,27)(25,26)(28,29)(30,35)(31,42)(32,37)(33,46)(34,38)(36,43)(39,54)(40,49)(41,51)(44,52)(45,50)(47,53)(48,56)(55,58)(57,59);(12,14,17,24)(13,18,21,22)(15,23,16,25)(19,26,20,27)(28,30,34,41)(29,35,38,51)(31,39,44,57)(32,45,33,40)(36,48,53,58)(37,50,46,49)(42,54,52,59)(43,56,47,55);(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)(41,57)(42,46)(45,56)(49,54)(50,59)(51,58);(12,16,17,15)(13,20,21,19)(14,23,24,25)(18,26,22,27);(13,21)(18,22)(19,20)(26,27)(28,32,34,33)(29,37,38,46)(30,40,41,45)(31,43,44,47)(35,49,51,50)(36,52,53,42)(39,55,57,56)(48,54,58,59)539 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54910);