Finite Group DatabasebetaFinite Group Databasebeta| order | 31650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (D211⋊C3)⋊C25 |
| unambiguous semidirect product | (D211⋊C25)⋊C3 |
| unambiguous semidirect product | ((C211⋊C3)⋊C25)⋊C2 |
| derived, Sylow | C211 ⋊ C2×C3×C25 |
| Hall | (C211⋊C3)⋊C25 ⋊ C2 |
| Hall | D211⋊C25 ⋊ C3 |
| Hall | C211⋊C25 ⋊ C2×C3 |
| Hall | D211⋊C3 ⋊ C25 |
| Hall | C211⋊C3 ⋊ C2×C25 |
| Hall | D211 ⋊ C3×C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | (D211⋊C3)⋊C5 |
| commutator, hypocenter | C211 | C2×C3×C25 |
| Fitting, socle, cosocle | C5×C211 | C2×C3×C5 |
| prime radical | C5×D211⋊C3 | C5 |
| LCS | G ▷ C211 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5275 |
Polycyclic presentation:
2,3,5,211,5|c^5=e,d^a=d^210,d^b=d^196,d^c=d^107185 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31650, 18);