Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#33401 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C11 | C22×D4 |
| commutator | C4 | C23×C8×C11 |
| Frattini, cosocle | C2×C8 | C24×C11 |
| socle | C2×C11 | C22×C4⋊C8 |
| prime radical | C2×C11×#41 | C2×C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C11 ◁ C2×C11×#131 ◁ G | |
684 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)(12,13,17,23,18,22,28,38,19,24,27,20,16,33,14,25)(15,21,31,37,32,36,40,43,29,35,41,34,30,42,26,39);(12,14,16,27,19,28,18,17)(13,20,22,25,24,23,33,38)(15,26,30,41,29,40,32,31)(21,34,36,39,35,37,42,43);(12,15)(13,21)(14,26)(16,30)(17,31)(18,32)(19,29)(20,34)(22,36)(23,37)(24,35)(25,39)(27,41)(28,40)(33,42)(38,43);(15,29)(21,35)(26,40)(30,32)(31,41)(34,37)(36,42)(39,43)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26389);