Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2215 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×C11×#2254 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C11 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
558 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37);(3,4,6,8)(5,9,10,7)(12,16)(13,20)(14,21)(17,22)(18,26)(19,25)(23,24);(3,5,6,10)(4,7,8,9);(11,12,17,26,14,18,13,16,15,19,20,24,21,23,22,25)836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26713);