Finite Group DatabasebetaFinite Group Databasebeta| order | 31650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1 |
| direct product | C3×D211⋊C25 |
| unambiguous semidirect product | (C3×D211)⋊C25 |
| derived, Sylow | C211 ⋊ C2×C3×C25 |
| Hall | C3×C211⋊C25 ⋊ C2 |
| Hall | C211⋊C25 ⋊ C2×C3 |
| Hall | C3×D211 ⋊ C25 |
| Hall | C3×C211 ⋊ C2×C25 |
| Hall | D211 ⋊ C3×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | D211⋊C5 |
| commutator, hypocenter | C211 | C2×C3×C25 |
| Frattini | C5 | C3×D211⋊C5 |
| Fitting, socle | C3×C5×C211 | C2×C5 |
| prime radical | C3×C5×D211 | C5 |
| cosocle | C5×C211 | C2×C3×C5 |
| LCS | G ▷ C211 | |
| UCS | C1 ◁ C3×C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15825 |
465 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31650, 12);