Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C22 |
| direct product | D3×C7×SD16 |
| Fitting | C3×C7×SD16 ⋊ C2 |
| Hall | C3×C7 ⋊ C2×SD16 |
| Sylow | C3 ⋊ C2×C7×SD16 |
136 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
147 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D7×SD16, D3×#6477, D3×#6478, … |
| maximal normal subgroup of | D3×D7×SD16, D3×#6477, D3×#6478, … |
| maximal quotient of | C7×#4760, C7×#4761, C7×#4762, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 892);