Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C3×C7×M16 ⋊ C2 |
| Hall | C3×C7 ⋊ #100 |
| Sylow | C7 ⋊ #823 |
| Sylow | C3 ⋊ #6397 |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
Polycyclic presentation:
2^5,3,7|b^2=c,c^2=e,b^a=bd,c^a=ce,f^a=f^2,g^a=g^6,d^b=de111 conjugacy classes — view the full character table.
| maximal subgroup of | #13053554, #13053555, #13053561, … |
| maximal normal subgroup of | #13053554, #13053555, #13053561, … |
| maximal quotient of | #13051369, #13051371, #13051387, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 244);