Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33469 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#33471 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C2×#442 |
| commutator | C8 | C23×C4×C11 |
| Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C2×C11×#509 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ C11×#405 ◁ G | |
668 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)(14,23,27,40)(15,29)(16,20)(17,30)(18,22)(19,26,36,43)(21,31)(24,41,35,32)(25,39,28,37)(33,34)(38,42);(12,14)(13,19)(15,24)(16,25)(17,32)(18,27)(20,35)(21,37)(22,36)(23,33)(26,42)(28,29)(30,40)(31,43)(34,41)(38,39);(12,15,29,13,18,20,16,22)(14,24,28,19,27,35,25,36)(17,33,42,38,34,30,31,21)(23,26,39,41,40,43,37,32);(12,16,18,29)(13,20,22,15)(14,25,27,28)(17,31,34,42)(19,35,36,24)(21,33,38,30)(23,39,40,37)(26,32,43,41)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26459);