Finite Group DatabasebetaFinite Group Databasebeta| order | 16650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×#66524⋊C2 |
| unambiguous semidirect product | #66524⋊(C2×C25) |
| derived, Sylow | C37 ⋊ C2×C9×C25 |
| Hall | C25×#66524 ⋊ C2 |
| Hall | C25×D37 ⋊ C9 |
| Hall | C25×C37 ⋊ C2×C9 |
| Hall | #66524 ⋊ C2×C25 |
| Hall | D37 ⋊ C9×C25 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8325 |
900 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C25×#13050613, #45685746, D25×#66524⋊C2, … |
| maximal normal subgroup of | C25×#13050613, #45685746, D25×#66524⋊C2, … |
| maximal quotient of | C25×#13050607, C2×C25×#66524⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16650, 2);