Finite Group DatabasebetaFinite Group Databasebeta| order | 18150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×#10624391 |
| Fitting, Hall | C112×C25 ⋊ D3 |
| derived, Hall | C112⋊C3 ⋊ C2×C25 |
| Hall | C25×C112⋊C3 ⋊ C2 |
| Sylow | C112 ⋊ D3×C25 |
39 conjugacy classes of subgroups.
| transitive degree | μt(G) = 825 |
950 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C25×#10624391⋊C2, #10624391⋊D25, D25×#10624391, … |
| maximal normal subgroup of | C25×#10624391⋊C2, #10624391⋊D25, D25×#10624391, … |
| maximal quotient of | C25×#13089712, C2×C25×#10624391 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18150, 69);