Finite Group DatabasebetaFinite Group Databasebeta| order | 18150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | D15×#10597243 |
| unambiguous semidirect product | C3⋊(D5×#10597243) |
| unambiguous semidirect product | C5⋊(D3×#10597243) |
| Fitting, socle, derived | C3×C5×C112 ⋊ C2×C5 |
| Hall | C3×C5×#10597243 ⋊ C2 |
| Hall | C5×#10597243 ⋊ D3 |
| Hall | C3×C112 ⋊ C5×D5 |
| Sylow | C112 ⋊ C5×D15 |
| Sylow | C3 ⋊ D5×#10597243 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C112 | C2×C5 |
| LCS | G ▷ C3×C5×C112 | |
| UCS | C1 | |
280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1815 |
261 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D15×#11925892, D15×#11925895, D3×D5×#10597243, … |
| maximal normal subgroup of | D15×#11925892, D15×#11925895, D3×D5×#10597243, … |
| maximal quotient of | Dic15×#10597243, C2×D15×#10597243 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18150, 156);