Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C7 ⋊ SD32 |
| Sylow | C7 ⋊ #828 |
| Sylow | C3 ⋊ #6374 |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 336 |
Polycyclic presentation:
2^5,3,7|a^2=e,b^2=cd,c^2=d,d^2=e,b^a=bc,c^a=cde,d^a=de,g^a=g^6,f^b=f^290 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#6374, #13052198, #13052209, … |
| maximal normal subgroup of | D3×#6374, #13052198, #13052209, … |
| maximal quotient of | #13050923, #13050926, #13050972, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 60);