Finite Group DatabasebetaFinite Group Databasebeta| order | 3528 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×C4⋊#64424 |
| Fitting | C3×C4×C72 ⋊ C2×C3 |
| Hall | C3×#3861 ⋊ D4 |
| Hall | C4⋊(C7⋊D7) ⋊ C32 |
| Sylow | C72 ⋊ C32×D4 |
480 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 588 |
141 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D4×#64424, D3×C4⋊#64424, #72245946, … |
| maximal normal subgroup of | C3×D4×#64424, D3×C4⋊#64424, #72245946, … |
| maximal quotient of | C2×C3×C4⋊#64424 |
Past the SmallGroups library coverage — no SmallGroups id.