Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | #67⋊Dic7 |
| Hall | C3×C7 ⋊ C4×D4 |
| Sylow | C7 ⋊ #67⋊C4 |
| Sylow | C3 ⋊ D4×Dic7 |
188 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 336 |
Polycyclic presentation:
2^5,3,7|a^2=d,c^a=ce,g^a=g^6,c^b=ce,f^b=f^284 conjugacy classes — view the full character table.
| maximal subgroup of | #13058010, #13058011, #13058017, … |
| maximal normal subgroup of | #13058010, #13058011, #13058017, … |
| maximal quotient of | #13053889, #13053899, #13053908, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 704);