Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#23751 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | C2×#124 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C2×C11 | C2×#400 |
| prime radical | C24×C11 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
664 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)(12,13,16,20,17,21,23,32)(14,22,25,34,26,37,31,18)(15,27,30,41,29,19,35,36)(24,38,39,40,28,42,43,33);(12,14,23,25,17,26,16,31)(13,18,32,22,21,34,20,37)(15,28,35,43,29,24,30,39)(19,33,41,38,27,40,36,42);(12,15,16,30,17,29,23,35)(13,19,20,36,21,27,32,41)(14,24,25,39,26,28,31,43)(18,33,22,38,34,40,37,42);(15,29)(19,27)(24,28)(30,35)(33,40)(36,41)(38,42)(39,43)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16739);