Finite Group DatabasebetaFinite Group Databasebeta| order | 37062 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C29 · Schur multiplier (H2) = C3 |
| direct product | C29×C3⋊D213 |
| unambiguous semidirect product | C3⋊(C29×D213) |
| unambiguous semidirect product | C71⋊(C3⋊D3×C29) |
| Fitting, socle, Hall | C32×C29×C71 ⋊ C2 |
| derived, Hall | C32×C71 ⋊ C2×C29 |
| Hall | C29×C71 ⋊ C3⋊D3 |
| Hall | C32×C29 ⋊ D71 |
| Sylow | C71 ⋊ C3⋊D3×C29 |
| Sylow | C32 ⋊ C29×D71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | C3⋊D213 |
| commutator, cosocle, hypocenter | C32×C71 | C2×C29 |
| Frattini | C1 | G |
| Fitting, socle | C32×C29×C71 | C2 |
| LCS | G ▷ C32×C71 | |
| UCS | C1 ◁ C29 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18531 |
9309 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37062, 18);