Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| isoclinism | isoclinic class of Dic14 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×C4×C22⋊D7 |
| Fitting | C22×C3×C4×C7 ⋊ C2 |
| Hall | C3×C7 ⋊ C4×D4 |
| Sylow | C7 ⋊ C3×C4×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 |
204 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊C8×C22⋊D7, #13054157, (C22⋊D7)⋊(C3⋊C8), … |
| maximal normal subgroup of | C3⋊C8×C22⋊D7, #13054157, (C22⋊D7)⋊(C3⋊C8), … |
| maximal quotient of | C3×C4×Dic7⋊C4, C3×#89705, C3×C4×(C2×D7)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 821);