Finite Group DatabasebetaFinite Group Databasebeta| order | 1040 |
| isoclinism | isoclinic class of #63122 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Hall | C5×C13 ⋊ C2×C8 |
| Sylow | C13 ⋊ D5⋊C8 |
| Sylow | C5 ⋊ D13⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #63122 |
| commutator, hypocenter | C5×C13 | C2×C8 |
| Frattini | C2 | C2×#63122 |
| Fitting | C4×C5×C13 | C4 |
| socle | C2×C5×C13 | C2×C4 |
| prime radical | C2×D65 | C4 |
| cosocle | Dic65 | C22 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C4 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 520 |
Polycyclic presentation:
2^4,5,13|a^2=c,b^2=d,c^2=d,e^a=e^3,f^a=f^8,e^c=e^4,f^c=f^1280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1040, 127);