Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#33689 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #3109 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C11×#575 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C4×C11×M16 ◁ G | |
520 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,21)(14,22,24,40)(15,27,28,43)(16,32,30,20)(18,33,35,25)(19,37,38,31)(23,39,26,42)(29,34,41,36);(15,28)(19,38)(22,40)(25,33)(27,43)(29,41)(31,37)(39,42);(12,14)(13,18)(15,29)(16,23)(17,24)(19,39)(20,34)(21,35)(22,27)(25,31)(26,30)(28,41)(32,36)(33,37)(38,42)(40,43);(14,23,24,26)(15,28)(18,34,35,36)(19,38)(22,39,40,42)(25,29,33,41)(27,43)(31,37)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26677);