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×#61941 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| prime radical | C11×#3219 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#533 ◁ G | |
1646 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)(28,29,33,36)(30,34,39,48)(31,41,43,51)(32,44,46,37)(35,45,50,42)(38,52,53,59)(40,56,55,49)(47,57,58,54);(12,14,17,24)(13,18,21,22)(15,23,16,25)(19,26,20,27)(28,30)(29,34)(31,38)(32,40)(33,39)(35,47)(36,48)(37,49)(41,52)(42,54)(43,53)(44,56)(45,57)(46,55)(50,58)(51,59);(12,15,17,16)(13,19,21,20)(14,23,24,25)(18,26,22,27)(28,31,33,43)(29,35,36,50)(30,38,39,53)(32,45,46,42)(34,47,48,58)(37,51,44,41)(40,57,55,54)(49,59,56,52);(12,16,17,15)(13,20,21,19)(14,23,24,25)(18,26,22,27)(29,36)(30,39)(35,50)(37,44)(38,53)(40,55)(41,51)(54,57);(13,21)(18,22)(19,20)(26,27)(30,39)(34,48)(38,53)(40,55)(47,58)(49,56)(52,59)(54,57)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54929);