Finite Group DatabasebetaFinite Group Databasebeta| order | 1260 |
| isoclinism | isoclinic class of D5×AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| derived, Hall | C5×C7 ⋊ C22×C9 |
| Hall | C5×C7⋊C9 ⋊ C22 |
| Hall | D5×D7 ⋊ C9 |
| Hall | C7⋊C9 ⋊ C2×D5 |
| Sylow | C7 ⋊ C2×C9×D5 |
| Sylow | C5 ⋊ C2×D7⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D5×AGL(1,𝔽7) |
| commutator, hypocenter | C5×C7 | C22×C9 |
| Fitting, socle, cosocle | C3×C5×C7 | C22×C3 |
| prime radical | C3×D5×D7 | C3 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 315 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | D5×C11×D7⋊C9, D55×D7⋊C9, D5×C11⋊(D7⋊C9), … |
| maximal normal subgroup of | D5×C11×D7⋊C9, D5×C13×D7⋊C9, D5×C17×D7⋊C9, … |
| maximal quotient of | D5×C11×D7⋊C9, D55×D7⋊C9, D5×C11⋊(D7⋊C9), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1260, 15);