Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18930 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18972 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C11×#121 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
818 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,17)(15,22)(18,24)(19,23)(21,26)(25,27)(28,29,34,39)(30,35,42,50)(31,43,45,53)(32,38,33,37)(36,47,51,44)(40,54,56,58)(41,52,46,49)(48,55,59,57);(12,13,16,19)(14,18,20,25)(15,23,22,17)(21,27,26,24)(28,30)(29,35)(31,40)(32,41)(33,46)(34,42)(36,48)(37,49)(38,52)(39,50)(43,58)(44,55)(45,56)(47,57)(51,59)(53,54);(12,14,16,20)(13,18,19,25)(15,21,22,26)(17,24,23,27)(28,31)(29,36)(30,40)(32,44)(33,47)(34,45)(35,48)(37,43)(38,53)(39,51)(41,55)(42,56)(46,57)(49,58)(50,59)(52,54);(14,20)(18,25)(21,26)(24,27)(28,32,34,33)(29,37,39,38)(30,41,42,46)(31,44,45,47)(35,49,50,52)(36,43,51,53)(40,55,56,57)(48,58,59,54)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11960);