Finite Group DatabasebetaFinite Group Databasebeta| order | 1680 |
| isoclinism | isoclinic class of C3⋊(C7⋊AGL(1,𝔽5)) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×C3⋊(C7⋊#170) |
| unambiguous semidirect product | (C2×C3)⋊(C7⋊#170) |
| unambiguous semidirect product | (C2×C7)⋊(C3⋊#170) |
| derived, Hall | C3×C5×C7 ⋊ C2×C8 |
| Hall | C5×C7 ⋊ C2×C3⋊C8 |
| Hall | C3×C7 ⋊ C2×#170 |
| Hall | C3×C5 ⋊ C2×C7⋊C8 |
| Sylow | C7 ⋊ C2×C3⋊#170 |
| Sylow | C5 ⋊ C2×C3⋊(C7⋊C8) |
| Sylow | C3 ⋊ C2×C7⋊#170 |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1680 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1680, 648);