Finite Group DatabasebetaFinite Group Databasebeta| order | 13950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D1395 |
| unambiguous semidirect product | C5⋊(C5×D279) |
| unambiguous semidirect product | C9⋊(C5×D155) |
| Fitting, Hall | C52×C9×C31 ⋊ C2 |
| derived | C5×C9×C31 ⋊ C2×C5 |
| Hall | C52×C31 ⋊ D9 |
| Hall | C9×C31 ⋊ C5×D5 |
| Hall | C52×C9 ⋊ D31 |
| Sylow | C31 ⋊ C5×D45 |
| Sylow | C52 ⋊ D279 |
| Sylow | C9 ⋊ C5×D155 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D1395 |
| commutator, cosocle, hypocenter | C5×C9×C31 | C2×C5 |
| Frattini | C3 | C5×D465 |
| Fitting | C52×C9×C31 | C2 |
| socle | C3×C52×C31 | D3 |
| LCS | G ▷ C5×C9×C31 | |
| UCS | C1 ◁ C5 | |
60 conjugacy classes of subgroups.
3495 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D31×D45, C5×D5×D279, C5×D9×D155, … |
| maximal normal subgroup of | C5×D31×D45, C5×D5×D279, C5×D9×D155, … |
| maximal quotient of | C5×Dic1395, C2×C5×D1395 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13950, 86);