Finite Group DatabasebetaFinite Group Databasebeta| order | 1960 |
| isoclinism | isoclinic class of AGL(1,𝔽5)×D49 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | AGL(1,𝔽5)×D49 |
| unambiguous semidirect product | (AGL(1,𝔽5)×C49)⋊C2 |
| unambiguous semidirect product | (C49⋊AGL(1,𝔽5))⋊C2 |
| Fitting, derived, Hall | C5×C49 ⋊ C2×C4 |
| Sylow | C49 ⋊ C2×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C5×C49 | C2×C4 |
| Frattini | C7 | D7×AGL(1,𝔽5) |
| socle | C5×C7 | C4×D7 |
| prime radical | D5×D49 | C2 |
| cosocle | D5×C49 | C22 |
| LCS | G ▷ C5×C49 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 54 |
| transitive degree | μt(G) = 245 |
130 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×D49⋊C7, AGL(1,𝔽5)×D49⋊C3 |
| maximal normal subgroup of | AGL(1,𝔽5)×D49⋊C7, AGL(1,𝔽5)×D49⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1960, 32);