Finite Group DatabasebetaFinite Group Databasebeta| order | 1040 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C5×D4×C13 ⋊ C2 |
| Hall | C5×C13 ⋊ D8 |
| Sylow | C13 ⋊ #686 |
| Sylow | C5 ⋊ #6104 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊D65 |
| commutator, cosocle | C4×C5×C13 | C22 |
| Frattini | C4 | C2×D65 |
| Fitting | C5×D4×C13 | C2 |
| socle | C2×C5×C13 | D4 |
| hypercenter | D4 | D65 |
| hypocenter | C5×C13 | D8 |
| LCS | G ▷ C4×C5×C13 ▷ C2×C5×C13 ▷ C5×C13 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D4 | |
44 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 520 |
Polycyclic presentation:
2^4,5,13|c^2=d,b^a=bc,c^a=cd,e^a=e^4,f^a=f^12,c^b=cd167 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1040, 79);