Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C2×D4×AGL(1,𝔽7) |
| unambiguous semidirect product | D7⋊(C2×C3×D4) |
| unambiguous semidirect product | (C2×D4×D7)⋊C3 |
| Fitting | C2×C7×D4 ⋊ C2×C3 |
| Hall | C2×D4×D7 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C22×D4 |
| Sylow | C7 ⋊ C22×C3×D4 |
472 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 175 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 56 |
70 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 1093);