Finite Group DatabasebetaFinite Group Databasebeta| order | 31302 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C47⋊(D37⋊C3)) |
| unambiguous semidirect product | C47⋊(C3⋊(D37⋊C3)) |
| unambiguous semidirect product | (C37⋊C3)⋊D141 |
| unambiguous semidirect product | D5217⋊C3 |
| Fitting, socle, derived | C3×C37×C47 ⋊ C2×C3 |
| Hall | C3×C47×C37⋊C3 ⋊ C2 |
| Hall | C37×C47 ⋊ C3×D3 |
| Hall | C3×C37⋊C3 ⋊ D47 |
| Sylow | C47 ⋊ C3⋊(D37⋊C3) |
| Sylow | C37 ⋊ C3×D141 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C37×C47 | C2×C3 |
| LCS | G ▷ C3×C37×C47 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5217 |
Polycyclic presentation:
2,3^2,37,47|c^a=c^2,d^a=d^36,e^a=e^46,d^b=d^261062 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31302, 22);