Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23387 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#23749 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C24×C11 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G | |
782 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,18)(14,19,15,17)(20,21)(22,24)(23,25)(26,27)(28,29)(30,34)(31,40)(32,35)(33,36)(37,41)(38,42)(39,43);(12,14,16,15)(13,17,18,19)(20,22,23,26)(21,24,25,27)(28,30)(29,34)(31,38)(32,41)(33,39)(35,37)(36,43)(40,42);(12,15,16,14)(13,17,18,19)(21,25)(24,27)(28,29)(30,37)(31,35)(32,40)(33,36)(34,41)(38,43)(39,42);(28,31,33,32)(29,35,36,40)(30,38,39,41)(34,37,43,42)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16737);