Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×SD32 |
| unambiguous semidirect product | (C7×SD32)⋊C3 |
| Fitting, Hall | C7×SD32 ⋊ C3 |
| Sylow | C7 ⋊ C3×SD32 |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 112 |
55 conjugacy classes — view the full character table.
| maximal subgroup of | SD32×AGL(1,𝔽7), #89686⋊C3, #89687⋊C3, … |
| maximal normal subgroup of | SD32×AGL(1,𝔽7), #89686⋊C3, #89687⋊C3, … |
| maximal quotient of | ΓL(1,𝔽8)×#357, ΓL(1,𝔽8)×#358, ΓL(1,𝔽8)×#367, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 132);