Finite Group DatabasebetaFinite Group Databasebeta| order | 18582 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C19⋊C3)⋊D163 |
| Fitting, socle, derived, Hall | C19×C163 ⋊ C2×C3 |
| Hall | C19⋊C3×C163 ⋊ C2 |
| Hall | D3097 ⋊ C3 |
| Sylow | C163 ⋊ D19⋊C3 |
| Hall | C19⋊C3 ⋊ D163 |
| Sylow | C19 ⋊ C3×D163 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C19×C163 | C2×C3 |
| LCS | G ▷ C19×C163 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3097 |
Polycyclic presentation:
2,3,19,163|c^a=c^18,d^a=d^162,c^b=c^7738 conjugacy classes — view the full character table.
| maximal subgroup of | D19⋊C3×D163, C2×(C19⋊C3)⋊D163 |
| maximal normal subgroup of | D19⋊C3×D163, C2×(C19⋊C3)⋊D163 |
| maximal quotient of | (C19⋊C3)⋊Dic163, C2×(C19⋊C3)⋊D163 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18582, 22);