Finite Group DatabasebetaFinite Group Databasebeta| order | 7056 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#11759644 |
| Fitting | C22×C32×C72 ⋊ C22 |
| Hall | C32×C72 ⋊ C2×D4 |
| Sylow | C72 ⋊ #3811 |
| Sylow | C32 ⋊ C2×C7×C22⋊D7 |
784 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
672 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72222214, #72222259 |
| maximal normal subgroup of | #72222214, #72222259 |
Past the SmallGroups library coverage — no SmallGroups id.