Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C3×C7×Q16 ⋊ C2 |
| Hall | C3×C7 ⋊ SD32 |
| Sylow | C7 ⋊ #828 |
| Sylow | C3 ⋊ #6402 |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 336 |
Polycyclic presentation:
2^5,3,7|b^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^2,g^a=g^6,c^b=cd,d^b=de81 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#828, #13053668, D3×#6402, … |
| maximal normal subgroup of | D7×#828, #13053668, D3×#6402, … |
| maximal quotient of | #13051394, #13051395, #13051468, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 249);