Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1913 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#10940 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #386 |
| commutator | C23 | C2×C42×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C24×C11 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
898 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(16,17)(18,22,27,34)(19,23)(20,31)(21,24)(25,32)(26,38,39,33)(28,42,41,35)(29,37)(30,44)(36,43)(40,45,47,46);(16,18,20,28,21,27,32,41)(17,22,25,35,24,34,31,42)(19,26,30,40,29,39,43,47)(23,33,36,45,37,38,44,46);(12,13,14,15)(16,19,21,29)(17,23,24,37)(18,26,27,39)(20,30,32,43)(22,33,34,38)(25,36,31,44)(28,40,41,47)(35,45,42,46)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3928);