Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17405 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#21883 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C24×C11 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C11×#117 ◁ G | |
954 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,16)(14,18)(20,21,25,29,24,28,38,45)(22,30,33,47,32,26,40,42)(23,34,37,46,36,27,39,44)(31,41,48,50,35,43,49,51);(12,13)(14,17)(15,16)(18,19)(20,22)(21,26)(23,35)(24,32)(25,33)(27,43)(28,30)(29,42)(31,36)(34,41)(37,49)(38,40)(39,48)(44,51)(45,47)(46,50);(13,16)(17,19)(20,23,24,36)(21,27,28,34)(22,31,32,35)(25,39,38,37)(26,41,30,43)(29,46,45,44)(33,49,40,48)(42,51,47,50);(12,14,15,18)(13,17,16,19)(21,28)(22,32)(27,34)(29,45)(31,35)(33,40)(44,46)(48,49)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 14871);