Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | Q16×AGL(1,𝔽7) |
| unambiguous semidirect product | D7⋊(C3×Q16) |
| unambiguous semidirect product | (D7×Q16)⋊C3 |
| Fitting | C7×Q16 ⋊ C2×C3 |
| Hall | D7×Q16 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C2×Q16 |
| Sylow | C7 ⋊ C2×C3×Q16 |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 112 |
49 conjugacy classes — view the full character table.
| maximal subgroup of | SD32×AGL(1,𝔽7), #89687⋊C3, Q32×AGL(1,𝔽7), … |
| maximal normal subgroup of | SD32×AGL(1,𝔽7), #89687⋊C3, Q32×AGL(1,𝔽7), … |
| maximal quotient of | #89564⋊C3, #89566⋊C3, #89565⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 335);