Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C7 ⋊ #103 |
| Sylow | C7 ⋊ #816 |
| Sylow | C3 ⋊ #6390 |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 672 |
Polycyclic presentation:
2^5,3,7|a^2=d,b^2=cd,c^2=e,b^a=bc,c^a=ce,f^a=f^2,g^a=g^6174 conjugacy classes — view the full character table.
| maximal subgroup of | #13052979, #13052981, #13052988, … |
| maximal normal subgroup of | #13052979, #13052981, #13052988, … |
| maximal quotient of | #13051367, #13051374, #13051388, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 237);