Finite Group DatabasebetaFinite Group Databasebeta| order | 14670 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×#13091814⋊C2 |
| unambiguous semidirect product | #13091814⋊(C2×C5) |
| Fitting, socle, Hall | C5×C163 ⋊ C2×C9 |
| derived, Sylow | C163 ⋊ C2×C5×C9 |
| Hall | C5×#13091814 ⋊ C2 |
| Hall | C5×D163 ⋊ C9 |
| Hall | #13091814 ⋊ C2×C5 |
| Hall | D163 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #13091814⋊C2 |
| commutator, hypocenter | C163 | C2×C5×C9 |
| Frattini | C1 | G |
| Fitting, socle | C5×C163 | C2×C9 |
| prime radical | C5×D163⋊C3 | C3 |
| cosocle | C163⋊C3 | C2×C3×C5 |
| LCS | G ▷ C163 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 815 |
135 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#13091814⋊C2, C2×C5×#13091814⋊C2 |
| maximal normal subgroup of | D5×#13091814⋊C2, C2×C5×#13091814⋊C2 |
| maximal quotient of | C5×#13091814⋊C4, C2×C5×#13091814⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14670, 14);