Finite Group DatabasebetaFinite Group Databasebeta| order | 31434 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C31×C169 ⋊ C2×C3 |
| Hall | #30628398 ⋊ C2 |
| Hall | C31×D169 ⋊ C3 |
| Hall | D169 ⋊ C31⋊C3 |
| Sylow | C169 ⋊ C2×C31⋊C3 |
| Sylow | C31 ⋊ D169⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C31×C169 | C2×C3 |
| Frattini | C13 | #14559027 |
| socle | C13×C31 | D13⋊C3 |
| LCS | G ▷ C31×C169 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5239 |
Polycyclic presentation:
2,3,13,31,13|c^13=e^12,c^a=c^12e,e^a=e^12,c^b=c^3e^2,d^b=d^5,e^b=e^3894 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31434, 20);