Finite Group DatabasebetaFinite Group Databasebeta| order | 16650 |
| isoclinism | isoclinic class of D37 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52×C9 · Schur multiplier (H2) = C5 |
| direct product | C52×C9×D37 |
| Fitting, Hall | C52×C9×C37 ⋊ C2 |
| derived, Sylow | C37 ⋊ C2×C52×C9 |
| Hall | C52×C37 ⋊ C2×C9 |
| Hall | C9×C37 ⋊ C2×C52 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8325 |
4500 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×C9×#3866, C5×C9×#10625194, C5×C9×D5×D37, … |
| maximal normal subgroup of | C52×C9×#3866, C5×C9×#10625194, C5×C9×D5×D37, … |
| maximal quotient of | C52×C9×Dic37, C2×C52×C9×D37 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16650, 54);