Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1909 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#10950 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #386 |
| commutator | C2×C4 | C2×C42×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C2×C11 | #1437 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
904 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)(14,23,26,19)(15,27)(16,31)(17,22)(18,21)(20,29)(24,38,39,43)(25,34,32,35)(28,41)(30,36)(33,40,37,42);(12,14,17,25,18,26,16,32)(13,19,22,35,21,23,31,34)(15,24,30,40,28,39,29,42)(20,33,27,38,36,37,41,43);(12,15,16,29,18,28,17,30)(13,20,22,27,21,36,31,41)(14,24,32,42,26,39,25,40)(19,33,35,38,23,37,34,43)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3938);