Finite Group DatabasebetaFinite Group Databasebeta| order | 4704 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | #99×#3861 |
| Fitting, Hall | C72×#99 ⋊ C3 |
| Sylow | C72 ⋊ C3×#99 |
520 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 132 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 392 |
209 conjugacy classes — view the full character table.
| maximal subgroup of | #99×#64424, B(4,𝔽2)×#3861, #72246176, … |
| maximal normal subgroup of | #99×#64424, B(4,𝔽2)×#3861, #72246176, … |
Past the SmallGroups library coverage — no SmallGroups id.