Finite Group DatabasebetaFinite Group Databasebeta| order | 13950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D15×C31⋊C3 |
| unambiguous semidirect product | C3⋊(C5×D5×C31⋊C3) |
| unambiguous semidirect product | C5⋊(C5×D3×C31⋊C3) |
| unambiguous semidirect product | (C5×D15×C31)⋊C3 |
| Fitting, socle | C3×C52×C31 ⋊ C2×C3 |
| derived | C3×C5×C31 ⋊ C2×C3×C5 |
| Hall | C3×C52×C31⋊C3 ⋊ C2 |
| Hall | C52×C31 ⋊ C3×D3 |
| Hall | C3×C31⋊C3 ⋊ C5×D5 |
| Sylow | C31 ⋊ C3×C5×D15 |
| Sylow | C52 ⋊ D3×C31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D15×C31⋊C3 |
| commutator, cosocle, hypocenter | C3×C5×C31 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C31 | C2×C3 |
| LCS | G ▷ C3×C5×C31 | |
| UCS | C1 ◁ C5 | |
96 conjugacy classes of subgroups.
585 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D15×D31⋊C3, C5×D15⋊(D31⋊C3), C5×D3×D5×C31⋊C3, … |
| maximal normal subgroup of | C5×D15×D31⋊C3, C5×D15⋊(D31⋊C3), C5×D3×D5×C31⋊C3, … |
| maximal quotient of | C5×Dic15×C31⋊C3, C2×C5×D15×C31⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13950, 131);