Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3290 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#23200 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | D42 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C23×C11 | H(5,𝔽2) |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C4×C11 ◁ G | |
878 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)(12,13,15,14)(16,17,21,26,23,27,22,37)(18,28,30,41,31,40,36,24)(19,32,33,42,34,45,20,25)(29,38,35,43,44,47,46,39);(12,14,15,13)(16,18,23,31)(17,24,27,41)(19,29,34,44)(20,35,33,46)(21,36,22,30)(25,38,42,47)(26,40,37,28)(32,39,45,43);(16,19,21,33,23,34,22,20)(17,25,37,45,27,42,26,32)(18,29,36,46,31,44,30,35)(24,38,28,43,41,47,40,39);(16,20,22,34,23,33,21,19)(17,25,37,45,27,42,26,32)(18,29,36,46,31,44,30,35)(24,39,40,47,41,43,28,38)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16188);