Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2230 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#13187 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #476 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C23×C11 | AGL(1,ℤ/8) |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C4×C8×C11 ◁ G | |
294 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)(13,15)(16,17)(18,28,32,46)(19,34)(20,24)(21,39)(22,27)(23,30,41,29)(25,36)(26,35)(31,44,33,45)(37,42,47,40)(38,43);(16,18,21,31,22,32,35,33)(17,23,26,40,27,41,39,42)(19,29,20,37,36,30,38,47)(24,28,34,45,43,46,25,44);(12,13,14,15)(16,19,35,38,22,36,21,20)(17,24,39,25,27,43,26,34)(18,29,33,47,32,30,31,37)(23,28,42,44,41,46,40,45)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6175);