Finite Group DatabasebetaFinite Group Databasebeta| order | 14670 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3 |
| Fitting, socle | C3×C5×C163 ⋊ C2×C3 |
| derived, Sylow | C163 ⋊ C2×C32×C5 |
| Hall | C3×C5×C163⋊C3 ⋊ C2 |
| Hall | C5×D163 ⋊ C32 |
| Hall | C3×C163⋊C3 ⋊ C2×C5 |
| Hall | C5×C163 ⋊ C2×C32 |
| Hall | D163 ⋊ C32×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | D163⋊C3 |
| commutator, cosocle, hypocenter | C163 | C2×C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C163 | C2×C3 |
| LCS | G ▷ C163 | |
| UCS | C1 ◁ C3×C5 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2445 |
495 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D5×D163⋊C3, C5×D3×D163⋊C3, D15×D163⋊C3, … |
| maximal normal subgroup of | C3×D5×D163⋊C3, C5×D3×D163⋊C3, D15×D163⋊C3, … |
| maximal quotient of | C3×C5×(C163⋊C3)⋊C4, C2×C3×C5×D163⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14670, 18);