Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #1426 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×#7463 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C11 | #367 |
| commutator | C16 | C2×C8×C11 |
| Frattini, cosocle | C4×C16 | C22×C11 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C42×C11 ◁ C4×C8×C11 ◁ C4×C11×C16 ◁ G | |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 2 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,16,15,17,18,19)(21,26,28,39)(22,31)(23,35)(24,36)(27,42)(29,43,46,51)(30,49,47,41)(32,37)(33,45)(34,44)(38,50,48,40);(20,21,27,43,23,29,22,26,36,47,31,40,32,38,42,49,25,28,45,51,37,46,34,39,24,30,44,50,35,48,33,41)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 451);