Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #465 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C11 · Schur multiplier (H2) = C22×C4 |
| direct product | C11×#8807 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C2×D4 |
| commutator | C2×C4 | C22×C8×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| socle, prime radical | C23×C11 | C2×C4⋊C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ C43×C11 ◁ G | |
422 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(16,17,18,20,19,21,22,23)(24,25)(26,32)(27,35)(28,30)(29,33)(31,36)(34,38)(37,39);(24,26,27,33,28,34,36,39)(25,29,31,32,30,37,35,38);(12,13,14,15)(25,30)(29,37)(31,35)(32,38)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1795);