Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #3415 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#33459 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator | C8 | C23×C4×C11 |
| Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C2×C11×#508 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#117 ◁ C11×#405 ◁ G | |
674 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 1408 |
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)(18,24)(19,27)(20,34)(21,25)(22,28)(23,30)(26,36)(29,43)(31,42)(32,40)(33,45)(35,41)(37,44)(38,47)(39,46);(16,18)(17,23)(19,29)(20,35)(21,32)(22,31)(24,34)(25,38)(26,40)(27,41)(28,39)(30,36)(33,46)(37,47)(42,44)(43,45);(12,14,15,13)(16,18)(17,24)(19,32)(20,30)(21,29)(22,31)(23,34)(25,43)(26,41)(27,40)(28,42)(33,47)(35,36)(37,46)(38,45)(39,44);(16,19,22,21)(17,25,28,27)(18,29,31,32)(20,33,37,36)(23,38,39,41)(24,40,42,43)(26,44,45,34)(30,35,46,47)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26447);