Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C7 ⋊ #108 |
| Sylow | C7 ⋊ #822 |
| Sylow | C3 ⋊ #6396 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
Polycyclic presentation:
2^5,3,7|a^2=d,b^2=c,c^2=e,d^2=e,b^a=bd,f^a=f^2,g^a=g^6,d^b=de114 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#822, D3×#6396, #13053550, … |
| maximal normal subgroup of | D7×#822, D3×#6396, #13053550, … |
| maximal quotient of | #13051383, #13051384, #13051462, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 243);