Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9091 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#9092 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #386 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C23×C11 | C4×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
456 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,18,15,14,17,19)(20,21)(22,31)(23,35,38,45)(24,39)(25,29)(26,30)(27,33)(28,37,44,36)(32,47,49,41)(34,42)(40,43)(46,48,51,50);(12,14,16,19,15,13,17,18)(20,22,24,33,26,34,25,40)(21,27,29,31,30,43,39,42)(23,32,37,50,38,49,36,48)(28,41,45,46,44,47,35,51);(13,14)(18,19)(20,23,26,38)(21,28,30,44)(22,32,34,49)(24,37,25,36)(27,41,43,47)(29,45,39,35)(31,46,42,51)(33,50,40,48)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 2080);