Finite Group DatabasebetaFinite Group Databasebeta| order | 18150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| direct product | D3×#15690028 |
| unambiguous semidirect product | C3⋊(C2×#15690028) |
| derived, Hall | C3×C112 ⋊ C2×C25 |
| Hall | C3×#15690028 ⋊ C2 |
| Hall | D3×C112 ⋊ C25 |
| Sylow | C112 ⋊ D3×C25 |
| Sylow | C3 ⋊ C2×#15690028 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | D3×#10597244 |
| commutator, hypocenter | C3×C112 | C2×C25 |
| Fitting, socle, cosocle | C3×C5×C112 | C2×C5 |
| prime radical | C5×D3×C112 | C5 |
| LCS | G ▷ C3×C112 | |
| UCS | C1 ◁ C5 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 825 |
435 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×#20258404, D3×#20258407, D3×#20258408, … |
| maximal normal subgroup of | D3×#20258404, D3×#20258407, D3×#20258408, … |
| maximal quotient of | Dic3×#15690028, C2×D3×#15690028 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18150, 66);