Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33657 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#33659 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C2×#481 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C11×#3060 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ C2×C11×#131 ◁ G | |
546 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)(16,29)(17,27)(18,22)(19,26)(21,32)(24,38)(25,40)(28,30)(31,37)(33,43)(34,41)(35,42)(36,39);(12,13)(14,19)(15,27)(16,30)(17,20)(18,22)(21,33)(23,39)(24,37)(25,36)(26,40)(28,29)(31,41)(32,43)(34,35)(38,42);(12,14,17,34,18,25,15,24)(13,19,20,35,22,36,27,37)(16,31,32,39,33,42,28,26)(21,38,29,40,30,41,43,23);(12,15,18,17)(13,20,22,27)(14,24,25,34)(16,28,33,32)(19,35,36,37)(21,29,30,43)(23,38,40,41)(26,42,39,31)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26647);