Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8603 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#11230 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #117 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C22×C11 | #380 |
| prime radical | C24×C11 | C2×Q8 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C22×C11×M16 ◁ G | |
622 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)(16,17,21,25,22,27,20,26)(18,28,31,39,32,38,30,23)(19,33,34,41,35,40,36,24)(29,37,43,46,44,47,45,42);(12,13)(14,15)(16,18,20,30,22,32,21,31)(17,23,25,28,27,39,26,38)(19,29,34,43,35,44,36,45)(24,37,40,42,41,47,33,46);(13,15)(16,19,20,34,22,35,21,36)(17,24,25,40,27,41,26,33)(18,29,30,43,32,44,31,45)(23,37,28,42,39,47,38,46)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4218);