Finite Group DatabasebetaFinite Group Databasebeta| order | 14460 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#11757210⋊C3 |
| unambiguous semidirect product | (C5×#11757210)⋊C3 |
| Fitting, socle, Hall | C5×C241 ⋊ C3×C4 |
| derived, Sylow | C241 ⋊ C3×C4×C5 |
| Hall | C5×#11757210 ⋊ C3 |
| Hall | C5×C241⋊C3 ⋊ C4 |
| Hall | #11757210 ⋊ C3×C5 |
| Hall | C241⋊C3 ⋊ C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #11757210⋊C3 |
| commutator, hypocenter | C241 | C3×C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C241 | C3×C4 |
| prime radical | C5×D241⋊C3 | C2 |
| cosocle | D241 | C2×C3×C5 |
| LCS | G ▷ C241 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
160 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14460, 28);