Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24292 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#24800 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×#135 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C4×C11 ◁ G | |
842 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)(16,17,21,27)(18,23,31,40)(19,32,35,43)(20,26,36,25)(22,30,38,29)(24,41,44,34)(28,45,33,37)(39,47,42,46);(16,18,20,29,21,31,36,30)(17,22,25,23,27,38,26,40)(19,28,34,46,35,33,41,47)(24,37,32,39,44,45,43,42);(13,15)(16,18)(17,23)(19,33)(20,29)(21,31)(22,26)(24,42)(25,38)(27,40)(28,35)(30,36)(32,37)(34,47)(39,44)(41,46)(43,45);(16,19,20,34,21,35,36,41)(17,24,25,32,27,44,26,43)(18,28,29,46,31,33,30,47)(22,37,23,39,38,45,40,42)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17788);