Finite Group DatabasebetaFinite Group Databasebeta| order | 19074 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C172 · Schur multiplier (H2) = C17 |
| direct product | C172×D33 |
| unambiguous semidirect product | C3⋊(C172×D11) |
| unambiguous semidirect product | C11⋊(D3×C172) |
| Fitting, socle, Hall | C3×C11×C172 ⋊ C2 |
| derived, Hall | C3×C11 ⋊ C2×C172 |
| Hall | C11×C172 ⋊ D3 |
| Hall | C3×C172 ⋊ D11 |
| Sylow | C11 ⋊ D3×C172 |
| Sylow | C3 ⋊ C172×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C172 | D33 |
| commutator, cosocle, hypocenter | C3×C11 | C2×C172 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C172 | C2 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C172 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9537 |
5202 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C17×D17×D33, D33×C17⋊D17, D3×C172×D11, … |
| maximal normal subgroup of | C17×D17×D33, D33×C17⋊D17, D3×C172×D11, … |
| maximal quotient of | C172×Dic33, C2×C172×D33 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19074, 18);