Finite Group DatabasebetaFinite Group Databasebeta| order | 34038 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C61 · Schur multiplier (H2) = C3 |
| direct product | C2×C3×C61×C31⋊C3 |
| unambiguous semidirect product | (C2×C31)⋊(C32×C61) |
| unambiguous semidirect product | (C2×C3×C31)⋊(C3×C61) |
| Fitting, socle | C2×C3×C31×C61 ⋊ C3 |
| derived, Sylow | C31 ⋊ C2×C32×C61 |
| Hall | C2×C31×C61 ⋊ C32 |
| Hall | C31×C61 ⋊ C2×C32 |
| Hall | C2×C31 ⋊ C32×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C61 | C31⋊C3 |
| commutator, cosocle, hypocenter | C31 | C2×C32×C61 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C31×C61 | C3 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C2×C3×C61 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11346 |
4758 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34038, 59);