Finite Group DatabasebetaFinite Group Databasebeta| order | 1960 |
| isoclinism | isoclinic class of D5×D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C2×C7×D5×D7 |
| unambiguous semidirect product | (C7×D5)⋊(C22×C7) |
| unambiguous semidirect product | (C5×D7)⋊(C22×C7) |
| unambiguous semidirect product | D35⋊(C22×C7) |
| Fitting, socle | C2×C5×C72 ⋊ C22 |
| derived | C5×C7 ⋊ C23×C7 |
| Hall | C5×C72 ⋊ C23 |
| Sylow | C72 ⋊ C22×D5 |
| Sylow | C5 ⋊ C22×C7×D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D5×D7 |
| commutator, cosocle, hypocenter | C5×C7 | C23×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C72 | C22 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C2×C7 | |
158 conjugacy classes of subgroups.
| transitive degree | μt(G) = 140 |
280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D5×D72, C2×C7×D7×AGL(1,𝔽5), C2×D7×C7⋊AGL(1,𝔽5), … |
| maximal normal subgroup of | C2×D5×D72, C2×C7×D7×AGL(1,𝔽5), C2×D7×C7⋊AGL(1,𝔽5), … |
| maximal quotient of | C7×D5×C22⋊D7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1960, 135);