Finite Group DatabasebetaFinite Group Databasebeta| order | 13950 |
| isoclinism | isoclinic class of D31 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C25 · Schur multiplier (H2) = C1 |
| direct product | C9×C25×D31 |
| Fitting, Hall | C9×C25×C31 ⋊ C2 |
| derived, Sylow | C31 ⋊ C2×C9×C25 |
| Hall | C25×C31 ⋊ C2×C9 |
| Hall | C9×C31 ⋊ C2×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9×C25 | D31 |
| commutator, hypocenter | C31 | C2×C9×C25 |
| Frattini | C3×C5 | C3×C5×D31 |
| Fitting | C9×C25×C31 | C2 |
| socle, cosocle | C3×C5×C31 | C2×C3×C5 |
| prime radical | C3×C5×D31 | C3×C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C9×C25 | |
36 conjugacy classes of subgroups.
3825 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×D25×D31, D9×C25×D31, D31×D225, … |
| maximal normal subgroup of | C9×D25×D31, D9×C25×D31, D31×D225, … |
| maximal quotient of | C9×C25×Dic31, C2×C9×C25×D31 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13950, 12);