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×#33456 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator | C8 | C23×C4×C11 |
| Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C22×C11×D16 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#117 ◁ C11×#405 ◁ G | |
718 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)(18,23)(19,22)(20,33)(21,24)(25,30)(26,31)(27,39)(28,34)(29,43)(32,35)(36,44)(37,42)(38,41)(40,46)(45,47);(17,22)(19,30)(20,31)(23,34)(24,35)(25,26)(28,42)(29,41)(32,44)(33,36)(37,38)(39,46)(40,47)(43,45);(12,14,15,13)(16,18)(17,23)(19,28)(20,29)(21,27)(22,34)(24,39)(25,37)(26,38)(30,42)(31,41)(32,40)(33,43)(35,46)(36,45)(44,47);(17,24)(18,27)(22,35)(25,36)(26,33)(28,40)(29,41)(42,47)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26444);