Finite Group DatabasebetaFinite Group Databasebeta| order | 31302 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | D47×#66524 |
| unambiguous semidirect product | C47⋊(C2×#66524) |
| derived, Hall | C37×C47 ⋊ C2×C9 |
| Hall | C47×#66524 ⋊ C2 |
| Hall | C37×D47 ⋊ C9 |
| Sylow | C47 ⋊ C2×#66524 |
| Sylow | C37 ⋊ C9×D47 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D47×C37⋊C3 |
| commutator, hypocenter | C37×C47 | C2×C9 |
| Fitting, socle, cosocle | C3×C37×C47 | C2×C3 |
| prime radical | C3×C37×D47 | C3 |
| LCS | G ▷ C37×C47 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15651 |
1125 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31302, 10);