Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2215 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C23×C4 |
| direct product | C11×#33697 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| socle | C22×C11 | C22×D8 |
| prime radical | C11×#3147 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
598 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)(22,29)(23,28)(24,30)(25,32)(26,31)(27,34)(33,41)(35,47)(36,43)(37,48)(38,44)(39,46)(40,49)(42,50)(45,51);(13,16)(17,19)(20,22,26,36,24,35,40,39,27,37,42,51,41,38,25,23)(21,28,32,44,33,45,50,48,34,46,49,47,30,43,31,29);(12,14,15,18)(13,17,16,19)(20,23,25,38,41,51,42,37,27,39,40,35,24,36,26,22)(21,29,31,43,30,47,49,46,34,48,50,45,33,44,32,28);(20,24,27,41)(21,30,34,33)(22,35,37,38)(23,36,39,51)(25,26,40,42)(28,43,46,45)(29,47,48,44)(31,49,50,32)836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26685);