Finite Group DatabasebetaFinite Group Databasebeta| order | 31302 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C47 · Schur multiplier (H2) = C3 |
| Fitting, socle | C3×C37×C47 ⋊ C2×C3 |
| derived, Sylow | C37 ⋊ C2×C32×C47 |
| Hall | C3×C47×C37⋊C3 ⋊ C2 |
| Hall | C47×D37 ⋊ C32 |
| Hall | C37×C47 ⋊ C2×C32 |
| Hall | C3×C37⋊C3 ⋊ C2×C47 |
| Hall | D37 ⋊ C32×C47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C47 | D37⋊C3 |
| commutator, cosocle, hypocenter | C37 | C2×C32×C47 |
| Frattini | C1 | G |
| Fitting, socle | C3×C37×C47 | C2×C3 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C3×C47 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5217 |
1692 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31302, 18);