Finite Group DatabasebetaFinite Group Databasebeta| order | 13950 |
| isoclinism | isoclinic class of C3⋊D75 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C31 · Schur multiplier (H2) = C3 |
| direct product | C31×C3⋊D75 |
| unambiguous semidirect product | C3⋊(C31×D75) |
| unambiguous semidirect product | C25⋊(C3⋊D3×C31) |
| Fitting, Hall | C32×C25×C31 ⋊ C2 |
| derived, Hall | C32×C25 ⋊ C2×C31 |
| Hall | C25×C31 ⋊ C3⋊D3 |
| Hall | C32×C31 ⋊ D25 |
| Sylow | C25 ⋊ C3⋊D3×C31 |
| Sylow | C32 ⋊ C31×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | C3⋊D75 |
| commutator, cosocle, hypocenter | C32×C25 | C2×C31 |
| Frattini | C5 | C31×C3⋊D15 |
| Fitting | C32×C25×C31 | C2 |
| socle | C32×C5×C31 | D5 |
| LCS | G ▷ C32×C25 | |
| UCS | C1 ◁ C31 | |
72 conjugacy classes of subgroups.
3534 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D31×C3⋊D75, C3⋊D3×C31×D25, D775⋊(C3⋊D3), … |
| maximal normal subgroup of | D31×C3⋊D75, C3⋊D3×C31×D25, D775⋊(C3⋊D3), … |
| maximal quotient of | C31×C3⋊Dic75, C2×C31×C3⋊D75 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13950, 47);