Finite Group DatabasebetaFinite Group Databasebeta| order | 4704 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C2×#72222022 |
| Fitting | C23×C72 ⋊ C22×C3 |
| Hall | C2×#11716115 ⋊ C3 |
| Hall | #3862 ⋊ C22×D4 |
| Sylow | C72 ⋊ C22×C3×D4 |
1011 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 1011 conjugacy classes of subgroups — too many to draw. Only its 202 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
104 conjugacy classes — view the full character table.
| maximal subgroup of | #72246028, #72246070, #72246136, … |
| maximal normal subgroup of | #72246028, #72246070, #72246136, … |
| maximal quotient of | #72245130, #72246070, #72246136 |
Past the SmallGroups library coverage — no SmallGroups id.