Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #6390⋊C3 |
| Hall | #6390 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ #103 |
| Sylow | C7 ⋊ C3×#103 |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^2,3,2^3,7|a^2=e,b^2=de,d^2=f,b^a=bd,d^a=df,g^a=g^6,g^c=g^458 conjugacy classes — view the full character table.
| maximal subgroup of | #89453⋊C3, C4×#1132⋊C3, #89469⋊C3, … |
| maximal normal subgroup of | #89453⋊C3, C4×#1132⋊C3, #89469⋊C3, … |
| maximal quotient of | #89251⋊C3, #89262⋊C3, #89277⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 26);