Finite Group DatabasebetaFinite Group Databasebeta| order | 31434 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×#30628398 |
| Fitting, Hall | C2×C31×C169 ⋊ C3 |
| derived, Hall | C31×C169 ⋊ C2×C3 |
| Hall | C2×C169 ⋊ C31⋊C3 |
| Sylow | C169 ⋊ C2×C31⋊C3 |
| Hall | C2×C31 ⋊ C169⋊C3 |
| Sylow | C31 ⋊ C2×C169⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #30628398 |
| commutator, cosocle, hypocenter | C31×C169 | C2×C3 |
| Frattini | C13 | C2×#11925881 |
| Fitting | C2×C31×C169 | C3 |
| socle | C2×C13×C31 | C13⋊C3 |
| LCS | G ▷ C31×C169 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10478 |
3498 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31434, 5);