Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9091 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#11059 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #386 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C24×C11 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
842 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)(16,17,21,27,22,25,20,26)(18,23,29,39,30,38,36,43)(19,31,34,41,35,24,33,42)(28,44,32,47,45,37,46,40);(12,13,14,15)(16,18)(17,23)(19,32)(20,36)(21,29)(22,30)(24,40)(25,38)(26,43)(27,39)(28,33)(31,47)(34,45)(35,46)(37,41)(42,44);(16,19,22,35)(17,24,25,31)(18,28,30,45)(20,34,21,33)(23,37,38,44)(26,42,27,41)(29,46,36,32)(39,47,43,40)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4047);