Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#23203 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | D42 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C22×D4×C11 | C23 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C4×C11 ◁ G | |
892 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,14)(16,17,22,27,23,28,21,26)(18,29,33,24,34,41,32,42)(19,35,36,44,37,43,20,25)(30,46,38,45,31,39,47,40);(12,14,15,13)(16,18,23,34)(17,24,28,42)(19,30,37,31)(20,38,36,47)(21,33,22,32)(25,39,44,46)(26,41,27,29)(35,45,43,40);(16,19,21,20,23,37,22,36)(17,25,27,35,28,44,26,43)(18,30,33,38,34,31,32,47)(24,39,29,45,42,46,41,40);(16,20,21,37,23,36,22,19)(17,25,26,43,28,44,27,35)(18,31,32,38,34,30,33,47)(24,40,29,39,42,45,41,46)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16191);