Finite Group DatabasebetaFinite Group Databasebeta| order | 31434 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C132×C31 ⋊ C2×C3 |
| Hall | C13×#11925882 ⋊ C2 |
| Hall | C31×C13⋊D13 ⋊ C3 |
| Hall | C13⋊D13 ⋊ C31⋊C3 |
| Sylow | C132 ⋊ C2×C31⋊C3 |
| Sylow | C31 ⋊ (C13⋊C3)⋊D13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C132×C31 | C2×C3 |
| LCS | G ▷ C132×C31 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1209 |
Polycyclic presentation:
2,3,13^2,31|c^a=c^12,d^a=d^12,c^b=c^3,e^b=e^25910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31434, 42);