Finite Group DatabasebetaFinite Group Databasebeta| order | 1040 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×AGL(1,𝔽5))⋊D13 |
| Hall | C5×C13 ⋊ C22⋊C4 |
| Sylow | C13 ⋊ C22⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ #6103 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | AGL(1,𝔽5)×D13 |
| commutator, Fitting, socle | C2×C5×C13 | C2×C4 |
| prime radical | C2×D5×D13 | C2 |
| cosocle | C2×D5×C13 | C22 |
| hypocenter | C5×C13 | C22⋊C4 |
| LCS | G ▷ C2×C5×C13 ▷ C5×C13 | |
| UCS | C1 ◁ C2 | |
68 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 260 |
Polycyclic presentation:
2^4,5,13|b^2=c,b^a=bd,f^a=f^12,e^b=e^2,e^c=e^474 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1040, 100);