Finite Group DatabasebetaFinite Group Databasebeta| order | 14520 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C3×#72213641 |
| derived, Sylow | C112 ⋊ C2×C3×C4×C5 |
| Hall | C3×#11757244 ⋊ C5 |
| Hall | C3×#10597243 ⋊ C2×C4 |
| Hall | #11757244 ⋊ C3×C5 |
| Hall | #10597243 ⋊ C2×C3×C4 |
| Hall | C3×C112 ⋊ C2×C4×C5 |
228 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 132 |
174 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#72213641, C3×#72213693, #72247295 |
| maximal normal subgroup of | D3×#72213641, C3×#72213693, #72247295 |
Past the SmallGroups library coverage — no SmallGroups id.