Finite Group DatabasebetaFinite Group Databasebeta| order | 4704 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#72228587 |
| Fitting | C2×C72×C8 ⋊ C2×C3 |
| Hall | C2×#11716061 ⋊ C3 |
| Hall | #3861 ⋊ C2×M16 |
| Sylow | C72 ⋊ C2×C3×M16 |
680 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 159 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 | C2×M16×#64424, C2×#72245150, C2×#72245156 |
| maximal normal subgroup of | C2×M16×#64424, C2×#72245150, C2×#72245156 |
Past the SmallGroups library coverage — no SmallGroups id.