Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#23472 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | C2×#124 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C2×C11 | C2×#393 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
1148 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)(14,19)(15,27,29,38)(16,21)(17,32)(18,22)(20,30,37,31)(23,36,39,43)(24,34)(25,35)(26,41)(28,33,40,42);(12,14)(13,19)(15,28,29,40)(16,25)(17,26)(18,24)(20,36,37,43)(21,35)(22,34)(23,31,39,30)(27,42,38,33)(32,41);(12,15)(13,20)(14,23)(16,31)(17,30)(18,29)(19,33)(21,38)(22,37)(24,39)(25,28)(26,40)(27,32)(34,42)(35,43)(36,41);(14,24)(19,34)(23,39)(25,26)(28,40)(33,42)(35,41)(36,43)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16460);