Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C3×C7×Q8 ⋊ C2 |
| Hall | C3×C7 ⋊ #137 |
| Sylow | C7 ⋊ #942 |
| Sylow | C3 ⋊ #6505 |
120 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 47 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|b^2=e,c^2=e,d^2=e,c^a=cd,d^a=de,f^a=f^2,g^a=g^6,c^b=ce,d^c=de111 conjugacy classes — view the full character table.
| maximal subgroup of | #13054724, #13054725, #13054726, … |
| maximal normal subgroup of | #13054724, #13054725, #13054726, … |
| maximal quotient of | #13056600, #13056602, #13056622, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 1007);