Finite Group DatabasebetaFinite Group Databasebeta| order | 4704 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×M16×#3861 |
| Fitting, Hall | C2×C72×M16 ⋊ C3 |
| Sylow | C72 ⋊ C2×C3×M16 |
680 conjugacy classes of subgroups; only the 330 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 330 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 784 |
380 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×M16×#64424, C2×AGL(1,ℤ/8)×#3861, C2×#72245153 |
| maximal normal subgroup of | C2×M16×#64424, C2×AGL(1,ℤ/8)×#3861, C2×#72245153 |
Past the SmallGroups library coverage — no SmallGroups id.