Finite Group DatabasebetaFinite Group Databasebeta| order | 31650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | (C5⋊D5)⋊(C211⋊C3) |
| Fitting, socle, derived, Hall | C52×C211 ⋊ C2×C3 |
| Hall | C52⋊(C211⋊C3) ⋊ C2 |
| Hall | C5⋊D5×C211 ⋊ C3 |
| Sylow | C211 ⋊ (C5⋊D5)⋊C3 |
| Hall | C5⋊D5 ⋊ C211⋊C3 |
| Sylow | C52 ⋊ C2×C211⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C211 | C2×C3 |
| LCS | G ▷ C52×C211 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3165 |
Polycyclic presentation:
2,3,5^2,211|c^a=c^4,d^a=d^4,c^b=cd^3,d^b=c^4d^3,e^b=e^14990 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31650, 37);