Finite Group DatabasebetaFinite Group Databasebeta| order | 18525 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×#10625203 |
| Fitting, Hall | C13×C19×C25 ⋊ C3 |
| derived, Hall | C13×C19 ⋊ C3×C25 |
| Hall | C19×C25 ⋊ C13⋊C3 |
| Hall | C13×C25 ⋊ C19⋊C3 |
| Sylow | C19 ⋊ C25×C13⋊C3 |
| Sylow | C13 ⋊ C25×C19⋊C3 |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6175 |
2125 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C25×#10625203, C25×#13093361, C25×#13093365, … |
| maximal normal subgroup of | C2×C25×#10625203, C25×#13093361, C25×#13093365, … |
| maximal quotient of | C2×C25×#10625203 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18525, 5);