Finite Group DatabasebetaFinite Group Databasebeta| order | 15030 |
| isoclinism | isoclinic class of D167 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×C9×D167 |
| unambiguous semidirect product | C167⋊(C2×C5×C9) |
| Fitting, Hall | C5×C9×C167 ⋊ C2 |
| derived, Sylow | C167 ⋊ C2×C5×C9 |
| Hall | C9×C167 ⋊ C2×C5 |
| Hall | C5×C167 ⋊ C2×C9 |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7515 |
3825 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×D5×D167, C5×D9×D167, D45×D167, … |
| maximal normal subgroup of | C9×D5×D167, C5×D9×D167, D45×D167, … |
| maximal quotient of | C5×C9×Dic167, C2×C5×C9×D167 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15030, 2);