Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33752 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#33798 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C11×#466 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
468 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)(14,20)(15,18)(16,19)(17,22)(21,26)(23,25)(24,27)(28,29)(30,34)(31,35)(32,45)(33,38)(36,42)(37,43)(39,46)(40,55)(41,49)(44,51)(47,52)(48,53)(50,56)(54,58)(57,59);(12,14,16,22)(13,17,19,20)(15,23,24,21)(18,26,27,25)(28,30,33,41)(29,34,38,49)(31,39,44,54)(32,40,43,53)(35,46,51,58)(36,47,50,57)(37,48,45,55)(42,52,56,59);(12,15,16,24)(13,18,19,27)(14,21,22,23)(17,25,20,26)(29,35)(31,42)(32,43)(34,46)(36,37)(38,51)(39,52)(40,53)(44,56)(45,50)(47,48)(49,58)(54,59)(55,57);(13,19)(17,20)(18,27)(25,26)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26786);