Finite Group DatabasebetaFinite Group Databasebeta| order | 31650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C5⋊(D211⋊C5)) |
| unambiguous semidirect product | C5⋊(C3⋊(D211⋊C5)) |
| unambiguous semidirect product | (C211⋊C5)⋊D15 |
| unambiguous semidirect product | D3165⋊C5 |
| Fitting, socle, derived | C3×C5×C211 ⋊ C2×C5 |
| Hall | C3×C5×C211⋊C5 ⋊ C2 |
| Hall | C5×C211⋊C5 ⋊ D3 |
| Hall | C3×C211 ⋊ C5×D5 |
| Sylow | C211 ⋊ C5×D15 |
| Sylow | C3 ⋊ C5⋊(D211⋊C5) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C211 | C2×C5 |
| LCS | G ▷ C3×C5×C211 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3165 |
Polycyclic presentation:
2,5,3,5,211|c^a=c^2,d^a=d^4,e^a=e^210,e^b=e^188360 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31650, 29);