Finite Group DatabasebetaFinite Group Databasebeta| order | 31650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C52 · Schur multiplier (H2) = C5 |
| Fitting, socle | C5×C211 ⋊ C2×C3×C5 |
| derived, Sylow | C211 ⋊ C2×C3×C52 |
| Hall | C5×(C211⋊C3)⋊C5 ⋊ C2 |
| Hall | C5×D211⋊C5 ⋊ C3 |
| Hall | C5×C211⋊C5 ⋊ C2×C3 |
| Hall | D211⋊C3 ⋊ C52 |
| Hall | C211⋊C3 ⋊ C2×C52 |
| Hall | D211 ⋊ C3×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | (D211⋊C3)⋊C5 |
| commutator, cosocle, hypocenter | C211 | C2×C3×C52 |
| Frattini | C1 | G |
| Fitting, socle | C5×C211 | C2×C3×C5 |
| LCS | G ▷ C211 | |
| UCS | C1 ◁ C5 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1055 |
185 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31650, 20);