Finite Group DatabasebetaFinite Group Databasebeta| order | 1680 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×(C22⋊D35)⋊C3 |
| unambiguous semidirect product | (C2×C22⋊D35)⋊C3 |
| Fitting | C23×C5×C7 ⋊ C2×C3 |
| Hall | C2×C22⋊D35 ⋊ C3 |
| Hall | C5×ΓL(1,𝔽8) ⋊ C2×D4 |
| Hall | C5×C7 ⋊ C2×C3×D4 |
| Hall | ΓL(1,𝔽8) ⋊ C2×C22⋊D5 |
| Sylow | C7 ⋊ C2×C3×C22⋊D5 |
| Sylow | C5 ⋊ C2×(C22⋊D7)⋊C3 |
216 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 280 |
118 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1680, 604);