Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19186 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#19226 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C11×#121 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
562 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)(12,13)(14,21)(15,20)(16,18)(17,24)(19,22)(23,27)(25,26)(28,29,33,37)(30,38,42,52)(31,35,43,49)(32,45,39,36)(34,46,48,41)(40,51,54,59)(44,56,53,50)(47,57,58,55);(13,18)(19,26)(20,24)(21,27)(28,30,39,46,33,42,32,41)(29,34,45,52,37,48,36,38)(31,40,53,57,43,54,44,55)(35,47,56,59,49,58,50,51);(12,14)(13,19)(15,22)(16,23)(17,25)(18,26)(20,27)(21,24)(28,31)(29,35)(30,40)(32,44)(33,43)(34,47)(36,50)(37,49)(38,51)(39,53)(41,55)(42,54)(45,56)(46,57)(48,58)(52,59);(12,15,16,17)(13,20,18,24)(14,22,23,25)(19,27,26,21)(31,43)(35,49)(40,54)(44,53)(47,58)(50,56)(51,59)(55,57)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 12214);