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 ⋊ #806 |
| Sylow | C3 ⋊ #6380 |
104 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 168 |
Polycyclic presentation:
2^5,3,7|a^2=c,b^2=cd,b^a=bd,d^a=de,g^a=g^6,c^b=ce,d^b=de,f^b=f^275 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#806, D3×#6380, #13052508, … |
| maximal normal subgroup of | D7×#806, D3×#6380, #13052508, … |
| maximal quotient of | #13050978, #13050981, #13050986, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 114);