Finite Group DatabasebetaFinite Group Databasebeta| order | 31302 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D5217 |
| unambiguous semidirect product | C37⋊(C3⋊D141) |
| unambiguous semidirect product | C47⋊(C3⋊D111) |
| Fitting, socle, derived, Hall | C32×C37×C47 ⋊ C2 |
| Hall | C37×C47 ⋊ C3⋊D3 |
| Hall | C32×C47 ⋊ D37 |
| Hall | C32×C37 ⋊ D47 |
| Sylow | C47 ⋊ C3⋊D111 |
| Sylow | C37 ⋊ C3⋊D141 |
| Sylow | C32 ⋊ D1739 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C37×C47 | C2 |
| LCS | G ▷ C32×C37×C47 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15651 |
Polycyclic presentation:
2,3^2,37,47|b^a=b^2,c^a=c^2,d^a=d^36,e^a=e^467827 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31302, 36);