Finite Group DatabasebetaFinite Group Databasebeta| order | 31210 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D3121⋊C5 |
| unambiguous semidirect product | (C3121⋊C5)⋊C2 |
| Fitting, socle, derived, Sylow | C3121 ⋊ C2×C5 |
| Hall | C3121⋊C5 ⋊ C2 |
| Hall | D3121 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3121 | C2×C5 |
| LCS | G ▷ C3121 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3121 |
Polycyclic presentation:
2,5,3121|c^a=c^3120,c^b=c^2163322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31210, 1);