Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24289 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#24798 |
| 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 | |
846 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)(18,23,31,39)(19,32,35,41)(20,26,33,25)(22,30,37,29)(24,40,42,34)(28,43,46,36)(38,45,47,44);(16,18,20,29,21,31,33,30)(17,22,25,23,27,37,26,39)(19,28,34,44,35,46,40,45)(24,36,32,38,42,43,41,47);(13,15)(16,18)(17,23)(19,28)(20,29)(21,31)(22,26)(24,38)(25,37)(27,39)(30,33)(32,43)(34,44)(35,46)(36,41)(40,45)(42,47);(16,19,33,40,21,35,20,34)(17,24,26,41,27,42,25,32)(18,28,30,45,31,46,29,44)(22,36,39,47,37,43,23,38)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17786);