Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C7 ⋊ Q32 |
| Sylow | C7 ⋊ #829 |
| Sylow | C3 ⋊ #6403 |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 42 |
| transitive degree | μt(G) = 672 |
Polycyclic presentation:
2^5,3,7|a^2=e,b^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^2,g^a=g^6,c^b=cd,d^b=de81 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#829, #13053674, D3×#6403, … |
| maximal normal subgroup of | D7×#829, #13053674, D3×#6403, … |
| maximal quotient of | #13051393, #13051396, #13051468, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 250);