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 ⋊ #6409 |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 672 |
Polycyclic presentation:
2^5,3,7|a^2=c,b^2=e,c^2=e,b^a=bcd,g^a=g^6,c^b=ce,f^b=f^284 conjugacy classes — view the full character table.
| maximal subgroup of | #13052278, #13052280, #13052297, … |
| maximal normal subgroup of | #13052278, #13052280, #13052297, … |
| maximal quotient of | #13050871, #13050887, #13050890, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 90);