Finite Group DatabasebetaFinite Group Databasebeta| order | 18150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C11 |
| direct product | C3×C5⋊#11925893 |
| unambiguous semidirect product | C5⋊(C3×#11925893) |
| Fitting, socle | C3×C5×C112 ⋊ C2×C5 |
| derived | C5×C112 ⋊ C2×C3×C5 |
| Hall | C3×C5×#10597245 ⋊ C2 |
| Hall | C5×#10597245 ⋊ C2×C3 |
| Hall | C3×C112 ⋊ C5×D5 |
| Sylow | C112 ⋊ C3×C5×D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C5⋊#11925893 |
| commutator, cosocle, hypocenter | C5×C112 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C112 | C2×C5 |
| LCS | G ▷ C5×C112 | |
| UCS | C1 ◁ C3 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 825 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#27130906, C3×#11925890⋊D5, C3×#11925896⋊D5, … |
| maximal normal subgroup of | C3×#27130906, C3×#11925890⋊D5, C3×#11925896⋊D5, … |
| maximal quotient of | C3×#27130852, C2×C3×C5⋊#11925893 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18150, 119);