Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2238 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#33656 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #481 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| socle | C2×C11 | C2×#481 |
| prime radical | C11×#3054 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C22×C4×C11 ◁ C22×C11×M16 ◁ G | |
556 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)(14,23)(15,20)(16,28)(17,32)(18,22)(19,26)(21,31)(24,38)(25,39)(27,37)(29,43)(30,36)(33,40)(34,41)(35,42);(16,29)(21,37)(23,39)(26,42)(27,31)(28,43)(30,41)(38,40);(12,14,17,33,18,25,15,24)(13,19,20,34,22,35,32,36)(16,30,31,42,29,41,27,26)(21,38,28,39,37,40,43,23);(12,15,18,17)(13,20,22,32)(14,24,25,33)(16,27,29,31)(19,34,35,36)(21,28,37,43)(23,38,39,40)(26,41,42,30)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26644);