Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #6389⋊C3 |
| Hall | #6389 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ #97 |
| Sylow | C7 ⋊ C3×#97 |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^2,3,2^3,7|a^2=d,b^2=e,e^2=f,b^a=bf,g^a=g^6,g^c=g^476 conjugacy classes — view the full character table.
| maximal subgroup of | #89307⋊C3, #89451⋊C3, C4×#1131⋊C3, … |
| maximal normal subgroup of | #89307⋊C3, #89451⋊C3, C4×#1131⋊C3, … |
| maximal quotient of | #89249⋊C3, #89250⋊C3, #89307⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 25);