Finite Group DatabasebetaFinite Group Databasebeta| order | 33174 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C97 · Schur multiplier (H2) = C1 |
| direct product | C97×C3⋊(D19⋊C3) |
| unambiguous semidirect product | C3⋊(C97×D19⋊C3) |
| unambiguous semidirect product | (C19⋊C3)⋊(D3×C97) |
| unambiguous semidirect product | D57⋊(C3×C97) |
| Fitting, socle | C3×C19×C97 ⋊ C2×C3 |
| derived | C3×C19 ⋊ C2×C3×C97 |
| Hall | C3×C19⋊C3×C97 ⋊ C2 |
| Hall | C19×C97 ⋊ C3×D3 |
| Hall | C3×C19⋊C3 ⋊ C2×C97 |
| Sylow | C19 ⋊ C3×D3×C97 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C97 | C3⋊(D19⋊C3) |
| commutator, cosocle, hypocenter | C3×C19 | C2×C3×C97 |
| Frattini | C1 | G |
| Fitting, socle | C3×C19×C97 | C2×C3 |
| LCS | G ▷ C3×C19 | |
| UCS | C1 ◁ C97 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5529 |
1746 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33174, 56);