Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #447 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C2×C4 |
| direct product | C11×#8189 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C11 | C2×D4 |
| commutator | C2×C4 | C2×C42×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| socle | C22×C11 | C4×C22⋊C4 |
| prime radical | C2×C11×#41 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
420 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,20,17,21,15,18)(14,19,23,26,24,27,22,25)(28,29)(30,33)(31,35)(32,34)(36,40)(37,39)(38,41)(42,43);(13,18,21,20)(19,25,27,26)(28,30,31,37,32,36,38,42)(29,33,35,39,34,40,41,43);(12,14,16,23,17,24,15,22)(13,19,20,26,21,27,18,25)(29,34)(30,36)(35,41)(37,42)836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1177);