Finite Group DatabasebetaFinite Group Databasebeta| order | 4704 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C2×Q8×#64424 |
| Fitting | C2×C72×Q8 ⋊ C2×C3 |
| Hall | C2×Q8×C7⋊D7 ⋊ C3 |
| Hall | #3861 ⋊ C22×Q8 |
| Sylow | C72 ⋊ C22×C3×Q8 |
1560 conjugacy classes of subgroups; only the 327 normal subgroups are shown.
This group has 1560 conjugacy classes of subgroups — too many to draw. Only its 327 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 784 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | C2×SD16×#64424, C2×#41×#64424 |
| maximal normal subgroup of | C2×SD16×#64424, C2×#41×#64424 |
Past the SmallGroups library coverage — no SmallGroups id.