Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2002 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#11218 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #120 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C22×C11 | #386 |
| prime radical | C24×C11 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G | |
638 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)(13,14)(16,17,21,25,22,27,20,26)(18,23,30,38,31,39,29,43)(19,32,34,24,35,41,36,42)(28,40,44,37,45,47,33,46);(12,13,15,14)(16,18)(17,23)(19,33)(20,29)(21,30)(22,31)(24,40)(25,38)(26,43)(27,39)(28,34)(32,46)(35,44)(36,45)(37,41)(42,47);(12,14,15,13)(16,19)(17,24)(18,28)(20,36)(21,34)(22,35)(23,37)(25,41)(26,32)(27,42)(29,33)(30,44)(31,45)(38,47)(39,46)(40,43)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4206);