Finite Group DatabasebetaFinite Group Databasebeta| order | 31950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C3 |
| direct product | C3⋊D15×C71⋊C5 |
| unambiguous semidirect product | C3⋊(D15×C71⋊C5) |
| unambiguous semidirect product | C5⋊(C3⋊D3×C71⋊C5) |
| unambiguous semidirect product | (C71×C3⋊D15)⋊C5 |
| Fitting, socle, derived | C32×C5×C71 ⋊ C2×C5 |
| Hall | C32×C5×C71⋊C5 ⋊ C2 |
| Hall | C5×C71⋊C5 ⋊ C3⋊D3 |
| Hall | C32×C71 ⋊ C5×D5 |
| Sylow | C71 ⋊ C5×C3⋊D15 |
| Sylow | C32 ⋊ D5×C71⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C5×C71 | C2×C5 |
| LCS | G ▷ C32×C5×C71 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3195 |
456 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31950, 68);