Finite Group DatabasebetaFinite Group Databasebeta| order | 34038 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C31 · Schur multiplier (H2) = C3 |
| direct product | C3×C31×D61⋊C3 |
| unambiguous semidirect product | D61⋊(C32×C31) |
| unambiguous semidirect product | (C61⋊C3)⋊(C2×C3×C31) |
| unambiguous semidirect product | (C3×D61)⋊(C3×C31) |
| Fitting, socle | C3×C31×C61 ⋊ C2×C3 |
| derived, Sylow | C61 ⋊ C2×C32×C31 |
| Hall | C3×C31×C61⋊C3 ⋊ C2 |
| Hall | C31×D61 ⋊ C32 |
| Hall | C31×C61 ⋊ C2×C32 |
| Hall | C3×C61⋊C3 ⋊ C2×C31 |
| Hall | D61 ⋊ C32×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C31 | D61⋊C3 |
| commutator, cosocle, hypocenter | C61 | C2×C32×C31 |
| Frattini | C1 | G |
| Fitting, socle | C3×C31×C61 | C2×C3 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C3×C31 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5673 |
1488 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34038, 30);