Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#22245 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C24 |
| commutator | C23 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle, prime radical | C23×C11 | C23×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ G | |
686 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(16,17)(18,25)(19,23)(20,29)(21,24)(22,27)(26,31)(28,30)(32,33,38,34,37,40,36,42)(35,39,44,41,45,47,46,43);(16,18)(17,22)(19,28)(20,26)(21,27)(23,31)(24,25)(29,30)(32,34,38,40,37,42,36,33)(35,43,44,39,45,41,46,47);(12,13,14,15)(16,19,21,20)(17,23,24,29)(18,26,27,28)(22,30,25,31)(32,35,37,45)(33,39,40,47)(34,41,42,43)(36,46,38,44);(16,20,21,19)(17,23,24,29)(18,26,27,28)(22,31,25,30)(32,36,37,38)(33,34,40,42)(35,44,45,46)(39,43,47,41)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 15233);