Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C7 ⋊ C4×Q8 |
| Sylow | C7 ⋊ #887 |
| Sylow | C3 ⋊ C4×Dic14 |
140 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 672 |
Polycyclic presentation:
2^5,3,7|a^2=d,b^2=e,c^2=de,c^a=cd,g^a=g^6,f^b=f^2102 conjugacy classes — view the full character table.
| maximal subgroup of | #13057714, C4×D3×Dic14, #13057726, … |
| maximal normal subgroup of | #13057714, C4×D3×Dic14, #13057726, … |
| maximal quotient of | #13053153, #13053157, #13053161, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 468);