Finite Group DatabasebetaFinite Group Databasebeta| order | 31302 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C47⋊(#66526⋊C2) |
| unambiguous semidirect product | #66526⋊D47 |
| Fitting, socle, derived, Hall | C37×C47 ⋊ C2×C9 |
| Hall | C47×#66526 ⋊ C2 |
| Hall | D1739 ⋊ C9 |
| Hall | #66526 ⋊ D47 |
| Sylow | C47 ⋊ #66526⋊C2 |
| Sylow | C37 ⋊ C9×D47 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C37×C47 | C2×C9 |
| prime radical | C47⋊(D37⋊C3) | C3 |
| cosocle | C47×C37⋊C3 | C2×C3 |
| LCS | G ▷ C37×C47 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1739 |
Polycyclic presentation:
2,3^2,37,47|b^3=c,d^a=d^36,e^a=e^46,d^b=d^16,d^c=d^26319 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31302, 15);