Finite Group DatabasebetaFinite Group Databasebeta| order | 1040 |
| isoclinism | isoclinic class of D5⋊#261 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×D5⋊#261 |
| unambiguous semidirect product | D5⋊(C2×#261) |
| unambiguous semidirect product | D13⋊(C2×AGL(1,𝔽5)) |
| unambiguous semidirect product | #63121⋊C22 |
| unambiguous semidirect product | #63122⋊C22 |
| Fitting, socle | C2×C5×C13 ⋊ C2×C4 |
| derived, Hall | C5×C13 ⋊ C22×C4 |
| Sylow | C13 ⋊ C22×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C22×#261 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D5⋊#261 |
| commutator, hypocenter | C5×C13 | C22×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C13 | C2×C4 |
| prime radical | C2×D5×D13 | C2 |
| cosocle | D65 | C23 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C2 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 130 |
44 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽5)×#261, C2×D5⋊AGL(1,𝔽13), #72246865, … |
| maximal normal subgroup of | C2×AGL(1,𝔽5)×#261, C2×D5⋊AGL(1,𝔽13) |
| maximal quotient of | #72246865, D3×D5⋊#261 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1040, 217);