Finite Group DatabasebetaFinite Group Databasebeta| order | 4704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×#72228714 |
| Fitting | C2×C72×D4 ⋊ C2×C3 |
| Hall | C2×#11716071 ⋊ C3 |
| Hall | #3861 ⋊ C2×D8 |
| Sylow | C72 ⋊ C2×C3×D8 |
760 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 784 |
122 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D8×#64424, C2×#72245150, C2×#72245156, … |
| maximal normal subgroup of | C2×D8×#64424, C2×#72245150, C2×#72245156, … |
Past the SmallGroups library coverage — no SmallGroups id.