Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| isoclinism | isoclinic class of AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×ΓL(1,𝔽8)⋊C16 |
| unambiguous semidirect product | (C2×ΓL(1,𝔽8))⋊C16 |
| unambiguous semidirect product | (C2×C7⋊C16)⋊C3 |
| derived, Sylow | C7 ⋊ C2×C3×C16 |
| Hall | C2×C7⋊C16 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C2×C16 |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 21);