Finite Group DatabasebetaFinite Group Databasebeta| order | 31974 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C732 ⋊ C2×C3 |
| Hall | #30630501 ⋊ C2 |
| Hall | C73×D73 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C732 | C2×C3 |
| LCS | G ▷ C732 | |
| UCS | C1 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 438 |
Polycyclic presentation:
2,3,73^2|c^a=c^72,c^b=c^8,d^b=d^64930 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31974, 14);