Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3198 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#22255 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C11 | C22×D4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C11×#376 ◁ G | |
666 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)(12,13,15,14)(16,17)(18,25)(19,23)(20,29)(21,24)(22,27)(26,31)(28,30)(34,40)(35,42)(37,43)(39,45)(41,46)(44,47);(12,14,15,13)(16,18)(17,22)(19,28)(20,26)(21,27)(23,31)(24,25)(29,30)(32,33)(34,37)(35,39)(36,38)(40,43)(41,44)(42,45)(46,47);(16,19,21,20)(17,23,24,29)(18,26,27,28)(22,30,25,31)(32,34,35,40,36,41,42,46)(33,37,39,43,38,44,45,47);(16,20,21,19)(17,23,24,29)(18,26,27,28)(22,31,25,30)(33,38)(34,41)(39,45)(40,46)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 15243);