Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19086 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#19092 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C11×#3219 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
816 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)(13,18)(14,21)(15,16)(20,23)(22,24)(25,27)(28,29)(30,38)(31,35)(32,44)(33,36)(34,41)(37,47)(39,55)(40,52)(42,53)(43,50)(45,49)(46,51)(48,57)(54,56)(58,59);(12,13)(14,19)(15,23)(16,18)(17,20)(21,27)(22,26)(24,25)(28,30,33,40)(29,34,36,49)(31,39,43,56)(32,45,47,41)(35,48,50,59)(37,52,44,38)(42,58,46,57)(51,54,53,55);(12,14,17,22)(13,19,20,26)(15,21,16,24)(18,25,23,27)(28,31,33,43)(29,35,36,50)(30,39,40,56)(32,46,47,42)(34,48,49,59)(37,53,44,51)(38,54,52,55)(41,58,45,57);(13,20)(18,23)(19,26)(25,27)(29,36)(30,40)(35,50)(37,44)(39,56)(41,45)(51,53)(57,58)341 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 12080);