Finite Group DatabasebetaFinite Group Databasebeta| order | 4704 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C2×C3×#11716115 |
| Fitting | C23×C3×C72 ⋊ C22 |
| Hall | C3×C72 ⋊ C22×D4 |
| Sylow | C72 ⋊ C22×C3×D4 |
1346 conjugacy classes of subgroups; only the 248 normal subgroups are shown.
This group has 1346 conjugacy classes of subgroups — too many to draw. Only its 248 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
456 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D3×#11716115, C2×C3×#72210376, C3×#72214319, … |
| maximal normal subgroup of | C2×D3×#11716115, C2×C3×#72210376, C3×#72214319, … |
| maximal quotient of | C3×#72214529 |
Past the SmallGroups library coverage — no SmallGroups id.