Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| isoclinism | isoclinic class of D7×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×D7×#170 |
| derived, Hall | C5×C7 ⋊ C22×C8 |
| Sylow | C7 ⋊ C22×#170 |
| Sylow | C5 ⋊ C2×C8×D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D7×AGL(1,𝔽5) |
| commutator, hypocenter | C5×C7 | C22×C8 |
| Frattini | C2 | C2×D7×AGL(1,𝔽5) |
| Fitting, socle | C22×C5×C7 | C2×C4 |
| prime radical | C22×C5×D7 | C4 |
| cosocle | C7×Dic5 | C23 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C22 | |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 560 |
100 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 935);