Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11855 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C2×C4 |
| direct product | C11×#11963 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#102 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C4×C8 | C23×C11 |
| prime radical | C11×#3147 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
396 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)(12,13,14,17,15,16,18,19)(20,21,25,30,23,32,39,29,26,31,42,47,40,28,24,41)(22,33,36,45,38,46,51,49,37,48,50,27,34,44,35,43);(13,16)(14,18)(20,22)(21,27)(23,34)(24,36)(25,35)(26,37)(28,43)(29,46)(30,48)(31,45)(32,49)(33,47)(38,40)(39,50)(41,44)(42,51);(13,16)(17,19)(20,23,26,40)(21,28,31,32)(22,34,37,38)(24,25,39,42)(27,43,45,49)(29,30,41,47)(33,46,48,44)(35,50,51,36)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4951);