Finite Group DatabasebetaFinite Group Databasebeta| order | 4704 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C2×#41×#3861 |
| Fitting, Hall | C2×C72×#41 ⋊ C3 |
| Sylow | C72 ⋊ C2×C3×#41 |
1640 conjugacy classes of subgroups; only the 770 normal subgroups are shown.
This group has 1640 conjugacy classes of subgroups — too many to draw. Only its 770 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×#41×#64424, C2×AGL(1,ℤ/8)×#3861, C2×#72245162 |
| maximal normal subgroup of | C2×#41×#64424, C2×AGL(1,ℤ/8)×#3861, C2×#72245162 |
Past the SmallGroups library coverage — no SmallGroups id.