Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18284 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#18303 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C24×C11 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
912 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,19)(14,20,22,27)(15,23,25,18)(17,24,26,21)(31,38)(33,39)(34,41)(36,42);(12,14,16,22)(13,17,19,26)(15,24,25,21)(18,27,23,20)(28,29)(30,33)(31,34)(32,35)(36,40)(37,39)(38,41)(42,43);(28,30)(29,33)(31,36)(32,37)(34,40)(35,39)(38,42)(41,43);(28,31,32,38)(29,34,35,41)(30,36,37,42)(33,40,39,43)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11291);