Finite Group DatabasebetaFinite Group Databasebeta| order | 15210 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×#15690151 |
| derived, Sylow | C132 ⋊ C2×C5×C9 |
| Hall | C5×#13095201 ⋊ C2 |
| Hall | C5×C13×D13 ⋊ C9 |
| Hall | #13095201 ⋊ C2×C5 |
| Hall | C5×C132 ⋊ C2×C9 |
| Hall | C13×D13 ⋊ C5×C9 |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1170 |
600 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#20258773, C5×#20258777, C5×#15690151⋊C2, … |
| maximal normal subgroup of | C5×#20258773, C5×#20258777, C5×#15690151⋊C2, … |
| maximal quotient of | C5×#20258755, C2×C5×#15690151 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15210, 38);