Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C7 ⋊ #99 |
| Sylow | C7 ⋊ #834 |
| Sylow | C3 ⋊ #6408 |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
Polycyclic presentation:
2^5,3,7|a^2=c,b^a=bd,d^a=de,f^a=f^2,g^a=g^6,c^b=ce111 conjugacy classes — view the full character table.
| maximal subgroup of | #13051023, #13051025, #13051029, … |
| maximal normal subgroup of | #13051023, #13051025, #13051029, … |
| maximal quotient of | #13051429, #13051431, #13051432, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 255);