Finite Group DatabasebetaFinite Group Databasebeta| order | 13950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×D279 |
| unambiguous semidirect product | C9⋊(C52×D31) |
| Fitting, Hall | C52×C9×C31 ⋊ C2 |
| derived, Hall | C9×C31 ⋊ C2×C52 |
| Hall | C52×C31 ⋊ D9 |
| Hall | C52×C9 ⋊ D31 |
| Sylow | C31 ⋊ C52×D9 |
| Sylow | C9 ⋊ C52×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | D279 |
| commutator, cosocle, hypocenter | C9×C31 | C2×C52 |
| Frattini | C3 | C52×D93 |
| Fitting | C52×C9×C31 | C2 |
| socle | C3×C52×C31 | D3 |
| LCS | G ▷ C9×C31 | |
| UCS | C1 ◁ C52 | |
96 conjugacy classes of subgroups.
3525 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×D9×D31, C5×D5×D279, C5×D45⋊D31, … |
| maximal normal subgroup of | C52×D9×D31, C5×D5×D279, C5×D45⋊D31, … |
| maximal quotient of | C52×Dic279, C2×C52×D279 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13950, 84);