Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24805 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#24807 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#525 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
844 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)(16,17,23,27,22,29,21,28)(18,30,39,26,20,38,32,24)(19,33,35,25,37,43,36,42)(31,41,45,44,34,40,46,47);(12,13)(14,15)(16,18,21,32,22,20,23,39)(17,24,27,30,29,26,28,38)(19,31,35,45,37,34,36,46)(25,40,33,44,42,41,43,47);(13,15)(16,19)(17,25)(18,31)(20,34)(21,35)(22,37)(23,36)(24,40)(26,41)(27,33)(28,43)(29,42)(30,44)(32,45)(38,47)(39,46);(16,20,23,32,22,18,21,39)(17,26,28,30,29,24,27,38)(19,34,36,45,37,31,35,46)(25,41,43,44,42,40,33,47)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17795);