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×#61946 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| prime radical | C11×#3221 | 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)(30,40)(31,44)(32,39)(33,37)(34,38)(35,43)(36,45)(41,55)(42,50)(46,53)(47,52)(48,51)(49,56)(54,58)(57,59);(12,14,17,24)(13,18,21,22)(15,23,16,25)(19,26,20,27)(28,30)(29,35)(31,41)(32,47)(33,43)(34,42)(36,49)(37,40)(38,52)(39,50)(44,59)(45,58)(46,57)(48,56)(51,54)(53,55);(12,15,17,16)(13,19,21,20)(14,23,24,25)(18,26,22,27)(28,31,33,46)(29,36,37,51)(30,41,43,57)(32,45,34,48)(35,49,40,54)(38,44,39,53)(42,56,47,58)(50,55,52,59);(12,16,17,15)(13,20,21,19)(14,23,24,25)(18,26,22,27)(29,37)(35,40)(36,51)(38,39)(44,53)(49,54)(50,52)(55,59);(13,21)(18,22)(19,20)(26,27)(28,32,33,34)(29,38,37,39)(30,42,43,47)(31,45,46,48)(35,50,40,52)(36,44,51,53)(41,56,57,58)(49,55,54,59)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54934);