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 ⋊ #800 |
| Sylow | C3 ⋊ #6401 |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 336 |
Polycyclic presentation:
2^5,3,7|a^2=c,c^2=de,d^2=e,b^a=bce,g^a=g^6,c^b=cd,d^b=de,f^b=f^272 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#800, #13052196, #13052206, … |
| maximal normal subgroup of | D7×#800, #13052196, #13052206, … |
| maximal quotient of | #13050922, #13050930, #13050970, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 61);