Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33522 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#33679 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#117 ◁ C11×#405 ◁ G | |
558 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,17)(15,16)(18,19)(20,21)(22,26)(23,27)(24,37)(25,30)(28,34)(29,35)(31,39)(32,38)(33,47)(36,43)(40,46)(41,45)(42,48)(44,49)(50,51);(13,16)(17,19)(20,22,25,31)(21,26,30,39)(23,32,36,44)(24,33,35,45)(27,38,43,49)(28,40,42,50)(29,41,37,47)(34,46,48,51);(21,27)(23,34)(24,35)(26,38)(28,29)(30,43)(32,46)(33,45)(36,48)(37,42)(39,49)(40,41)(44,51)(47,50);(12,14,15,18)(13,17,16,19)(22,31)(26,39)(32,44)(33,45)(38,49)(40,50)(41,47)(46,51)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26667);