Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×ΓL(1,𝔽8)⋊C4 |
| unambiguous semidirect product | (C2×ΓL(1,𝔽8))⋊(C4×C7) |
| unambiguous semidirect product | (C2×Dic7)⋊(C3×C7) |
| derived | C7 ⋊ C2×C3×C4×C7 |
| Hall | C2×C7×Dic7 ⋊ C3 |
| Hall | C7×ΓL(1,𝔽8) ⋊ C2×C4 |
| Sylow | C72 ⋊ C2×C3×C4 |
69 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
196 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 106);