Finite Group DatabasebetaFinite Group Databasebeta| order | 31950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C52 · Schur multiplier (H2) = C5 |
| Fitting, socle | C32×C5×C71 ⋊ C2×C5 |
| derived | C3×C71 ⋊ C2×C3×C52 |
| Hall | C32×C5×C71⋊C5 ⋊ C2 |
| Hall | C5×C71⋊C5 ⋊ C3×D3 |
| Hall | C3×D213 ⋊ C52 |
| Hall | C32×C71 ⋊ C2×C52 |
| Sylow | C71 ⋊ C3×C52×D3 |
| Sylow | C32 ⋊ C5×D71⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | C3⋊(D71⋊C5) |
| commutator, cosocle, hypocenter | C3×C71 | C2×C3×C52 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C71 | C2×C5 |
| LCS | G ▷ C3×C71 | |
| UCS | C1 ◁ C3×C5 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2130 |
540 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31950, 61);