Finite Group DatabasebetaFinite Group Databasebeta| order | 13950 |
| isoclinism | isoclinic class of D225 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×D225 |
| unambiguous semidirect product | C9⋊(C31×D25) |
| unambiguous semidirect product | C25⋊(D9×C31) |
| Fitting, Hall | C9×C25×C31 ⋊ C2 |
| derived, Hall | C9×C25 ⋊ C2×C31 |
| Hall | C25×C31 ⋊ D9 |
| Hall | C9×C31 ⋊ D25 |
| Sylow | C25 ⋊ D9×C31 |
| Sylow | C9 ⋊ C31×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D225 |
| commutator, cosocle, hypocenter | C9×C25 | C2×C31 |
| Frattini | C3×C5 | D15×C31 |
| Fitting | C9×C25×C31 | C2 |
| socle | C3×C5×C31 | D15 |
| LCS | G ▷ C9×C25 | |
| UCS | C1 ◁ C31 | |
36 conjugacy classes of subgroups.
3534 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D31×D225, D9×C31×D25, D225⋊D31, … |
| maximal normal subgroup of | D31×D225, D9×C31×D25, D225⋊D31, … |
| maximal quotient of | C31×Dic225, C2×C31×D225 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13950, 17);