Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2031 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#11285 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #124 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C22×C11 | #394 |
| prime radical | C24×C11 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G | |
606 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15)(16,17)(18,22,27,34)(19,23,30,37)(20,25)(21,24)(26,33)(28,35,41,46)(29,36)(31,38,43,44)(32,39)(40,45)(42,47);(16,18)(17,22,24,34)(19,29,30,42)(20,28)(21,27)(23,36)(25,35,39,46)(26,31,40,43)(32,41)(33,44)(37,47)(38,45);(16,19)(17,23,24,37)(18,26,27,40)(20,31)(21,30)(22,33)(25,38,39,44)(28,29,41,42)(32,43)(34,45)(35,36)(46,47)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4273);