Finite Group DatabasebetaFinite Group Databasebeta| order | 18150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1 |
| direct product | C2×C3×#15690028 |
| derived, Sylow | C112 ⋊ C2×C3×C25 |
| Hall | C2×C3×C112 ⋊ C25 |
| Hall | C3×C112 ⋊ C2×C25 |
| Hall | C2×C112 ⋊ C3×C25 |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1650 |
870 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#27130778, C3×#27130781, C3×#27130782, … |
| maximal normal subgroup of | C3×#27130778, C3×#27130781, C3×#27130782, … |
| maximal quotient of | C3×C4×#15690028, C22×C3×#15690028 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18150, 77);