Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3026 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#20962 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator | C23 | C23×C4×C11 |
| Frattini, cosocle | C24 | C24×C11 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1742 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)(13,15)(16,17)(18,22)(19,29,31,23)(20,32)(21,25)(24,33)(26,34,39,42)(27,40)(28,36)(30,37,44,43)(35,41)(38,46,47,45);(12,13,14,15)(16,18,21,28)(17,22,25,36)(19,26,31,39)(20,27,33,41)(23,34,29,42)(24,35,32,40)(30,38,44,47)(37,45,43,46);(16,19)(17,23)(18,26)(20,30)(21,31)(22,34)(24,37)(25,29)(27,38)(28,39)(32,43)(33,44)(35,45)(36,42)(40,46)(41,47);(16,20,21,33)(17,24,25,32)(18,27,28,41)(19,30,31,44)(22,35,36,40)(23,37,29,43)(26,38,39,47)(34,45,42,46)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 13950);