Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×D7×C4⋊C4 |
| Fitting | C3×C7×C4⋊C4 ⋊ C2 |
| Hall | C3×C7 ⋊ C2×C4⋊C4 |
| Sylow | C7 ⋊ C2×C3×C4⋊C4 |
184 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 336 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | #13052589, #13052591, #13052593, … |
| maximal normal subgroup of | #13052589, #13052591, #13052593, … |
| maximal quotient of | C3×#89439, C3×#89421, C3×#89422, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 784);