Finite Group DatabasebetaFinite Group Databasebeta| order | 8646 |
| automorphism | Aut(G) order 11239800 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4323 |
| unambiguous semidirect product | C3⋊D1441 |
| unambiguous semidirect product | C11⋊D393 |
| unambiguous semidirect product | C131⋊D33 |
| Fitting, socle, derived, Hall | C3×C11×C131 ⋊ C2 |
| Hall | C11×C131 ⋊ D3 |
| Hall | C3×C131 ⋊ D11 |
| Sylow | C131 ⋊ D33 |
| Hall | C3×C11 ⋊ D131 |
| Sylow | C11 ⋊ D393 |
| Sylow | C3 ⋊ D1441 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C11×C131 | C2 |
| LCS | G ▷ C3×C11×C131 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,11,131|b^a=b^2,c^a=c^10,d^a=d^1302163 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D33×D131, D11×D393, D3×D1441, … |
| maximal normal subgroup of | D33×D131, D11×D393, D3×D1441, … |
| maximal quotient of | Dic4323, C2×D4323, D12969, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8646, 8);