Finite Group DatabasebetaFinite Group Databasebeta| order | 13950 |
| isoclinism | isoclinic class of D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C31 · Schur multiplier (H2) = C3 |
| direct product | C32×C31×D25 |
| unambiguous semidirect product | C25⋊(C2×C32×C31) |
| Fitting, Hall | C32×C25×C31 ⋊ C2 |
| derived, Sylow | C25 ⋊ C2×C32×C31 |
| Hall | C25×C31 ⋊ C2×C32 |
| Hall | C32×C25 ⋊ C2×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C31 | D25 |
| commutator, cosocle, hypocenter | C25 | C2×C32×C31 |
| Frattini | C5 | C32×D5×C31 |
| Fitting | C32×C25×C31 | C2 |
| socle | C32×C5×C31 | D5 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C32×C31 | |
72 conjugacy classes of subgroups.
3906 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C31×#1035, C32×C31⋊#1035, C32×D25×D31, … |
| maximal normal subgroup of | C32×C31×#1035, C32×C31⋊#1035, C32×D25×D31, … |
| maximal quotient of | C32×C31×Dic25, C2×C32×C31×D25 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13950, 39);