Finite Group DatabasebetaFinite Group Databasebeta| order | 18054 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C3 |
| direct product | C17×C3⋊D177 |
| unambiguous semidirect product | C3⋊(C17×D177) |
| unambiguous semidirect product | C59⋊(C17×C3⋊D3) |
| Fitting, socle, Hall | C32×C17×C59 ⋊ C2 |
| derived, Hall | C32×C59 ⋊ C2×C17 |
| Hall | C17×C59 ⋊ C3⋊D3 |
| Hall | C32×C17 ⋊ D59 |
| Sylow | C59 ⋊ C17×C3⋊D3 |
| Sylow | C32 ⋊ C17×D59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C3⋊D177 |
| commutator, cosocle, hypocenter | C32×C59 | C2×C17 |
| Frattini | C1 | G |
| Fitting, socle | C32×C17×C59 | C2 |
| LCS | G ▷ C32×C59 | |
| UCS | C1 ◁ C17 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9027 |
4539 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C17×D177, D51⋊D177, C17×C3⋊D3×D59, … |
| maximal normal subgroup of | D3×C17×D177, D51⋊D177, C17×C3⋊D3×D59, … |
| maximal quotient of | C17×C3⋊Dic177, C2×C17×C3⋊D177 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18054, 12);