Finite Group DatabasebetaFinite Group Databasebeta| order | 15210 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×#15690148 |
| derived, Sylow | C132 ⋊ C2×C5×C9 |
| Hall | C5×#13095200 ⋊ C2 |
| Hall | C5×C13⋊D13 ⋊ C9 |
| Hall | #13095200 ⋊ C2×C5 |
| Hall | C5×C132 ⋊ C2×C9 |
| Hall | C13⋊D13 ⋊ C5×C9 |
192 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7605 |
510 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#20258768, C5×#20258770, C5×#15690148⋊C2, … |
| maximal normal subgroup of | C5×#20258768, C5×#20258770, C5×#15690148⋊C2, … |
| maximal quotient of | C5×#20258752, C2×C5×#15690148 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15210, 35);