Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #6432⋊C3 |
| Hall | #6432 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C4⋊Q8 |
| Sylow | C7 ⋊ C3×C4⋊Q8 |
136 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^3,3,2^2,7|a^2=f,b^2=f,c^2=e,b^a=bf,c^a=ce,g^a=g^6,g^d=g^458 conjugacy classes — view the full character table.
| maximal subgroup of | #89277⋊C3, #89276⋊C3, #89281⋊C3, … |
| maximal normal subgroup of | #89277⋊C3, #89276⋊C3, #89281⋊C3, … |
| maximal quotient of | #89428⋊C3, #89433⋊C3, #89452⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 287);