Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2018 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#11240 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #121 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C22×C11 | #380 |
| 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)(16,17,21,25,22,26,20,36)(18,27,30,38,31,41,29,23)(19,32,35,47,34,24,33,39)(28,42,45,37,44,40,43,46);(12,13)(14,15)(16,18,20,29,22,31,21,30)(17,23,25,27,26,38,36,41)(19,28,33,43,34,44,35,45)(24,37,39,40,32,46,47,42);(13,15)(16,19,20,33,22,34,21,35)(17,24,25,39,26,32,36,47)(18,28,29,43,31,44,30,45)(23,37,27,40,38,46,41,42)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4228);