Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D7×Dic3⋊C4 |
| Hall | C3×C7 ⋊ C2×C4⋊C4 |
| Sylow | C7 ⋊ C2×Dic3⋊C4 |
| Sylow | C3 ⋊ D7×C4⋊C4 |
184 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 336 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D7×Dic6, #13057716, #13057718, … |
| maximal normal subgroup of | C4×D7×Dic6, #13057716, #13057718, … |
| maximal quotient of | D7×#807, #13052758, D7×#808, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 536);