Finite Group DatabasebetaFinite Group Databasebeta| order | 10140 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C13 |
| direct product | C5×#14523129 |
| derived, Sylow | C132 ⋊ C3×C4×C5 |
| Hall | C5×#10621725 ⋊ C3 |
| Hall | C5×#92789 ⋊ C4 |
| Hall | C5×C132 ⋊ C3×C4 |
| Hall | #10621725 ⋊ C3×C5 |
| Hall | #92789 ⋊ C4×C5 |
72 conjugacy classes of subgroups.
340 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#14523128⋊C3, C3×C5×#14523129, C5×C3⋊#14523129 |
| maximal normal subgroup of | C5×#14523128⋊C3, C3×C5×#14523129 |
| maximal quotient of | C5×#20258753, C3×C5×#14523129, C5×C3⋊#14523129 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10140, 56);