Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| isoclinism | isoclinic class of D5×D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×C4×D5×D7 |
| Fitting | C2×C4×C5×C7 ⋊ C22 |
| derived, Hall | C5×C7 ⋊ C23×C4 |
| Sylow | C7 ⋊ C22×C4×D5 |
| Sylow | C5 ⋊ C22×C4×D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D5×D7 |
| commutator, hypocenter | C5×C7 | C23×C4 |
| Frattini | C2 | C22×D5×D7 |
| Fitting | C2×C4×C5×C7 | C22 |
| socle | C22×C5×C7 | C23 |
| prime radical | C22×D5×D7 | C2 |
| cosocle | C2×C5×C7 | C24 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C2×C4 | |
472 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 180 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 280 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C4×D5×AGL(1,𝔽7), C2×C4×D7×AGL(1,𝔽5), C2×D4×D5×D7, … |
| maximal normal subgroup of | C2×C4×D5×AGL(1,𝔽7), C2×C4×D7×AGL(1,𝔽5), C2×D4×D5×D7, … |
| maximal quotient of | D5×D7×M16, D5×D7×C22⋊C4 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 987);