Finite Group DatabasebetaFinite Group Databasebeta| order | 4704 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×C4⋊#64424 |
| Fitting | C42×C72 ⋊ C2×C3 |
| Hall | C4×C4⋊(C7⋊D7) ⋊ C3 |
| Hall | #3861 ⋊ C4×D4 |
| Sylow | C72 ⋊ C3×C4×D4 |
940 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 940 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 784 |
188 conjugacy classes — view the full character table.
| maximal subgroup of | #72259955, C4×D4×#64424, #72260102 |
| maximal normal subgroup of | #72259955, C4×D4×#64424, #72260102 |
| maximal quotient of | #72259955 |
Past the SmallGroups library coverage — no SmallGroups id.