Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2031 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#11237 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #124 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C22×C11 | #400 |
| prime radical | C24×C11 | C2×Q8 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ 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)(13,14)(16,17,21,25,22,26,20,36)(18,27,30,39,31,38,29,23)(19,32,34,41,35,47,33,24)(28,37,44,42,45,40,43,46);(12,13,15,14)(16,18,20,29,22,31,21,30)(17,23,25,27,26,39,36,38)(19,28,33,43,35,45,34,44)(24,40,32,46,41,37,47,42);(12,14,15,13)(16,19,20,33,22,35,21,34)(17,24,25,32,26,41,36,47)(18,28,29,43,31,45,30,44)(23,37,27,42,39,40,38,46)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4225);