Finite Group DatabasebetaFinite Group Databasebeta| order | 1680 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | Q8×C5⋊AGL(1,𝔽7) |
| Fitting | C5×C7×Q8 ⋊ C2×C3 |
| Hall | Q8×D35 ⋊ C3 |
| Hall | C5×ΓL(1,𝔽8) ⋊ C2×Q8 |
| Hall | C5×C7 ⋊ C2×C3×Q8 |
| Hall | ΓL(1,𝔽8) ⋊ Q8×D5 |
| Sylow | C7 ⋊ C3×Q8×D5 |
| Sylow | C5 ⋊ Q8×AGL(1,𝔽7) |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 280 |
85 conjugacy classes — view the full character table.
| maximal subgroup of | SL(2,𝔽3)×C5⋊AGL(1,𝔽7), Q8×D5×AGL(1,𝔽7), SD16×C5⋊AGL(1,𝔽7), … |
| maximal normal subgroup of | SL(2,𝔽3)×C5⋊AGL(1,𝔽7), Q8×D5×AGL(1,𝔽7), SD16×C5⋊AGL(1,𝔽7), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1680, 601);