Finite Group DatabasebetaFinite Group Databasebeta| order | 19074 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×#13181892 |
| Fitting, socle, Hall | C11×C172 ⋊ D3 |
| derived, Hall | C172⋊C3 ⋊ C2×C11 |
| Hall | C11×C172⋊C3 ⋊ C2 |
| Sylow | C172 ⋊ D3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | #13181892 |
| commutator, cosocle, hypocenter | C172⋊C3 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C172 | D3 |
| LCS | G ▷ C172⋊C3 | |
| UCS | C1 ◁ C11 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 561 |
825 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×#13181892⋊C2, D11×#13181892, #13181892⋊D11, … |
| maximal normal subgroup of | C11×#13181892⋊C2, D11×#13181892, #13181892⋊D11, … |
| maximal quotient of | C11×#16812392, C2×C11×#13181892 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19074, 10);