Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1705 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C22×C8 |
| direct product | C11×#9825 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C11 | #127 |
| commutator | C42 | C22×C4×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G | |
558 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)(12,13,14,15)(17,20)(18,21)(22,23)(24,25)(26,32)(27,29)(28,36)(30,35)(31,33)(34,38)(37,39);(13,15)(16,17,21,23,19,22,18,20)(25,29)(30,37)(31,36)(32,38);(24,26,33,39,27,34,28,35)(25,30,36,38,29,37,31,32)836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 2813);