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 ⋊ #104 |
| Sylow | C7 ⋊ #837 |
| 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,g^a=g^6,f^b=f^296 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#6379, #13052490, #13053361, … |
| maximal normal subgroup of | D3×#6379, #13052490, #13053361, … |
| maximal quotient of | #13050863, #13050869, #13050874, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 94);