Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#24462 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×#578 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C4×C11 ◁ G | |
1302 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)(12,13,14,15)(16,17,22,26)(18,28,31,38)(19,32,36,24)(20,30,23,39)(21,27,40,25)(29,45,47,42)(33,41,46,34)(35,43,37,44);(16,18,22,31)(17,23,26,20)(19,33,36,46)(21,39,40,30)(24,42,32,45)(25,38,27,28)(29,35,47,37)(34,43,41,44);(13,15)(16,19,22,36)(17,24,26,32)(18,29,31,47)(20,34,23,41)(21,35,40,37)(25,43,27,44)(28,42,38,45)(30,46,39,33);(16,20)(17,18)(19,34)(21,28)(22,23)(24,29)(25,39)(26,31)(27,30)(32,47)(33,43)(35,42)(36,41)(37,45)(38,40)(44,46)473 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17450);