Finite Group DatabasebetaFinite Group Databasebeta| order | 31446 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #30628422⋊C2 |
| Fitting, socle, derived, Sylow | C1747 ⋊ C2×C9 |
| Hall | #30628422 ⋊ C2 |
| Hall | D1747 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C1747 | C2×C9 |
| prime radical | D1747⋊C3 | C3 |
| cosocle | C1747⋊C3 | C2×C3 |
| LCS | G ▷ C1747 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1747 |
Polycyclic presentation:
2,3^2,1747|b^3=c,d^a=d^1746,d^b=d^412,d^c=d^371115 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31446, 8);