Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1902 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#10955 |
| 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 | |
900 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)(12,13,16,23,18,21,17,22)(14,19,26,34,25,35,31,33)(15,27,29,20,28,36,30,37)(24,38,39,32,40,41,42,43);(12,14,17,26,18,25,16,31)(13,19,23,33,21,35,22,34)(15,24,30,39,28,40,29,42)(20,32,36,38,37,43,27,41);(12,15,18,28)(13,20)(14,24,25,40)(16,29,17,30)(19,32)(21,37)(22,27)(23,36)(26,39,31,42)(33,38)(34,41)(35,43)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3943);