Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | #41×D35 |
| Fitting | C5×C7×#41 ⋊ C2 |
| Hall | C5×C7 ⋊ C2×#41 |
| Sylow | C7 ⋊ D5×#41 |
| Sylow | C5 ⋊ D7×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×D35 |
| commutator, socle, cosocle | C2×C5×C7 | C24 |
| Frattini | C2 | C23×D35 |
| Fitting | C5×C7×#41 | C2 |
| hypercenter | #41 | D35 |
| hypocenter | C5×C7 | C2×#41 |
| LCS | G ▷ C2×C5×C7 ▷ C5×C7 | |
| UCS | C1 ◁ C4 ◁ #41 | |
328 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 280 |
190 conjugacy classes — view the full character table.
| maximal subgroup of | #41×C5⋊AGL(1,𝔽7), D5×D7×#41, AGL(1,ℤ/8)×D35, … |
| maximal normal subgroup of | #41×C5⋊AGL(1,𝔽7), D5×D7×#41, AGL(1,ℤ/8)×D35, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 1067);