Finite Group DatabasebetaFinite Group Databasebeta| order | 18594 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C2×C1033⋊C9 |
| unambiguous semidirect product | (C2×C1033)⋊C9 |
| derived, Sylow | C1033 ⋊ C2×C9 |
| Hall | C2×C1033 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C1033⋊C3 |
| commutator, hypocenter | C1033 | C2×C9 |
| Frattini | C3 | C2×C1033⋊C3 |
| Fitting, socle, prime radical | C2×C3×C1033 | C3 |
| cosocle | C3×C1033 | C2×C3 |
| LCS | G ▷ C1033 | |
| UCS | C1 ◁ C2×C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18594 |
2082 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic1033⋊C9, C4×C1033⋊C9, C2×D1033⋊C9, … |
| maximal normal subgroup of | Dic1033⋊C9, C4×C1033⋊C9, C2×D1033⋊C9, … |
| maximal quotient of | C4×C1033⋊C9, C22×C1033⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18594, 3);