Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | D7×#208 |
| Hall | C3×C7 ⋊ C2×M16 |
| Sylow | C7 ⋊ C2×#208 |
| Sylow | C3 ⋊ D7×M16 |
136 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#805, #13052488, D7×#819, … |
| maximal normal subgroup of | D7×#805, #13052488, D7×#819, … |
| maximal quotient of | #13052225, #13052226, #13052246, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 426);