Finite Group DatabasebetaFinite Group Databasebeta| order | 33174 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C97 · Schur multiplier (H2) = C3 |
| direct product | C97×C3⋊D57 |
| unambiguous semidirect product | C3⋊(C97×D57) |
| unambiguous semidirect product | C19⋊(C3⋊D3×C97) |
| Fitting, socle, Hall | C32×C19×C97 ⋊ C2 |
| derived, Hall | C32×C19 ⋊ C2×C97 |
| Hall | C19×C97 ⋊ C3⋊D3 |
| Hall | C32×C97 ⋊ D19 |
| Sylow | C19 ⋊ C3⋊D3×C97 |
| Sylow | C32 ⋊ D19×C97 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C97 | C3⋊D57 |
| commutator, cosocle, hypocenter | C32×C19 | C2×C97 |
| Frattini | C1 | G |
| Fitting, socle | C32×C19×C97 | C2 |
| LCS | G ▷ C32×C19 | |
| UCS | C1 ◁ C97 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16587 |
8439 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33174, 83);