Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C4×C7×#67 |
| Fitting | C22×C3×C4×C7 ⋊ C2 |
| Hall | C3×C7 ⋊ C4×D4 |
| Sylow | C3 ⋊ C4×C7×D4 |
188 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 336 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | #67×C7⋊C8, #13054153, #67⋊(C7⋊C8), … |
| maximal normal subgroup of | #67×C7⋊C8, #13054153, #67⋊(C7⋊C8), … |
| maximal quotient of | C4×C7×Dic3⋊C4, C7×#4933, C4×C7×(C2×D3)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 907);