Finite Group DatabasebetaFinite Group Databasebeta| order | 33174 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D97⋊C9 |
| unambiguous semidirect product | D97⋊(C9×C19) |
| unambiguous semidirect product | (C97⋊C9)⋊(C2×C19) |
| derived, Sylow | C97 ⋊ C2×C9×C19 |
| Hall | C19×C97⋊C9 ⋊ C2 |
| Hall | C19×D97 ⋊ C9 |
| Hall | C19×C97 ⋊ C2×C9 |
| Hall | C97⋊C9 ⋊ C2×C19 |
| Hall | D97 ⋊ C9×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C19 | D97⋊C3 |
| commutator, hypocenter | C97 | C2×C9×C19 |
| Frattini | C3 | C19×D97⋊C3 |
| Fitting, socle | C3×C19×C97 | C2×C3 |
| prime radical | C3×C19×D97 | C3 |
| cosocle | C3×C97 | C2×C3×C19 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C3×C19 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16587 |
1254 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33174, 13);