Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| isoclinism | isoclinic class of AGL(1,𝔽5)×AGL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | AGL(1,𝔽5)×AGL(1,𝔽8) |
| unambiguous semidirect product | (C23×AGL(1,𝔽5))⋊C7 |
| Fitting, socle, derived | C23×C5 ⋊ C4×C7 |
| Hall | C23×AGL(1,𝔽5) ⋊ C7 |
| Sylow | C5 ⋊ C4×AGL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C23×C5 | C4×C7 |
| prime radical | D5×AGL(1,𝔽8) | C2 |
| cosocle | C23×D5 | C2×C7 |
| LCS | G ▷ C23×C5 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 40 |
40 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×AΓL(1,𝔽8), C2×AGL(1,𝔽5)×AGL(1,𝔽8) |
| maximal normal subgroup of | AGL(1,𝔽5)×AΓL(1,𝔽8), C2×AGL(1,𝔽5)×AGL(1,𝔽8) |
| maximal quotient of | C2×AGL(1,𝔽5)×AGL(1,𝔽8) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 1078);