Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C3×C42×C7 ⋊ C2 |
| Hall | C3×C7 ⋊ #104 |
| Sylow | C7 ⋊ #805 |
| Sylow | C3 ⋊ #6379 |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
Polycyclic presentation:
2^5,3,7|b^2=c,d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^2,g^a=g^6174 conjugacy classes — view the full character table.
| maximal subgroup of | #13052483, #13052484, #13052485, … |
| maximal normal subgroup of | #13052483, #13052484, #13052485, … |
| maximal quotient of | #13051355, #13051356, #13051366, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 226);