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×#33460 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator | C8 | C23×C4×C11 |
| Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C2×C11×#508 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#117 ◁ C11×#405 ◁ G | |
674 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 1408 |
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)(16,17,22,28)(18,30,19,25)(20,29,23,26)(21,36,38,44)(24,34,41,32)(27,35,45,39)(31,42,33,43)(37,46,47,40);(16,18,22,19)(17,24,28,41)(20,31,23,33)(21,37,38,47)(25,36,30,44)(26,40,29,46)(27,43,45,42)(32,35,34,39);(12,14,15,13)(16,19,22,18)(17,25,28,30)(20,31,23,33)(21,34,38,32)(24,36,41,44)(26,43,29,42)(27,40,45,46)(35,37,39,47);(16,20,22,23)(17,26,28,29)(18,31,19,33)(21,35,38,39)(24,40,41,46)(25,42,30,43)(27,44,45,36)(32,37,34,47)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26448);