Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13309 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#13466 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #469 |
| commutator, Frattini, cosocle | C22×C8 | C23×C11 |
| socle | C2×C11 | #2065 |
| prime radical | C2×C11×#135 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C22×C4×C11 ◁ C2×C4×C8×C11 ◁ G | |
314 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,20,25)(14,26)(15,32)(16,23,37,43)(17,22,18,40)(19,27,39,24)(21,34)(28,36)(29,42)(30,33)(31,41)(35,38);(12,14,16,28,19,30,17,38,20,31,37,32,39,21,18,29)(13,15,22,26,24,35,23,34,25,36,40,41,27,42,43,33);(12,15)(13,21)(14,27)(16,34)(17,26)(18,41)(19,42)(20,36)(22,28)(23,29)(24,31)(25,30)(32,40)(33,37)(35,39)(38,43)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6454);