Finite Group DatabasebetaFinite Group Databasebeta| order | 7056 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C3×C4⋊#64424 |
| Fitting | C2×C3×C4×C72 ⋊ C2×C3 |
| Hall | C2×C4⋊(C7⋊D7) ⋊ C32 |
| Hall | C3×#3861 ⋊ C2×D4 |
| Sylow | C72 ⋊ C2×C32×D4 |
1620 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1176 |
282 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×D4×#64424, C2×D3×C4⋊#64424, C2×#72245946 |
| maximal normal subgroup of | C2×C3×D4×#64424, C2×D3×C4⋊#64424, C2×#72245946 |
Past the SmallGroups library coverage — no SmallGroups id.