Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3019 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#20955 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1710 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)(13,15)(16,17,21,25,22,27,20,26)(18,28,30,23,32,38,31,39)(19,33,34,40,36,24,35,41)(29,42,45,46,44,47,43,37);(12,13,14,15)(16,18)(17,23)(19,29)(20,30)(21,31)(22,32)(24,37)(25,28)(26,38)(27,39)(33,46)(34,43)(35,45)(36,44)(40,42)(41,47);(16,19)(17,24)(18,29)(20,34)(21,35)(22,36)(23,37)(25,40)(26,41)(27,33)(28,42)(30,43)(31,45)(32,44)(38,47)(39,46);(16,20,22,21)(17,25,27,26)(18,30,32,31)(19,34,36,35)(23,28,39,38)(24,40,33,41)(29,43,44,45)(37,42,46,47)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 13943);