Finite Group DatabasebetaFinite Group Databasebeta| order | 15210 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×D13×C13⋊C9 |
| derived, Sylow | C132 ⋊ C2×C5×C9 |
| Hall | C5×C13×C13⋊C9 ⋊ C2 |
| Hall | C5×C13×D13 ⋊ C9 |
| Hall | C13×C13⋊C9 ⋊ C2×C5 |
| Hall | C5×C132 ⋊ C2×C9 |
| Hall | C13×D13 ⋊ C5×C9 |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1170 |
840 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#20258781, C5×D13×D13⋊C9, C5×#261×C13⋊C9, … |
| maximal normal subgroup of | C5×#20258781, C5×D13×D13⋊C9, C5×#261×C13⋊C9, … |
| maximal quotient of | C5×Dic13×C13⋊C9, C2×C5×D13×C13⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15210, 40);