Finite Group DatabasebetaFinite Group Databasebeta| order | 1960 |
| isoclinism | isoclinic class of C7⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×C7⋊AGL(1,𝔽5) |
| unambiguous semidirect product | D5⋊(C7×Dic7) |
| unambiguous semidirect product | (C2×C7)⋊(C7×AGL(1,𝔽5)) |
| Fitting, socle | C2×C5×C72 ⋊ C4 |
| derived | C5×C7 ⋊ C2×C4×C7 |
| Hall | C5×C72 ⋊ C2×C4 |
| Sylow | C72 ⋊ C2×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C2×C7×Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | C7⋊AGL(1,𝔽5) |
| commutator, hypocenter | C5×C7 | C2×C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C72 | C4 |
| prime radical | C2×C72×D5 | C2 |
| cosocle | C7×D5 | C22×C7 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C2×C7 | |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 140 |
238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1960, 130);