Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C128 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C5 ⋊ C128 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C64 | D5 |
| commutator, hypocenter | C5 | C128 |
| Fitting, cosocle | C5×C64 | C2 |
| socle, prime radical | C2×C5 | C64 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C64 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 133 |
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^7,5|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,f^2=g,h^a=h^4256 conjugacy classes — view the full character table.
| maximal subgroup of | D5×C128, C2×#10597919, #11987210, … |
| maximal normal subgroup of | D5×C128, C2×#10597919, #11987210, … |
| maximal quotient of | #11985825, C2×#10597919, C3×#10597919, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 1);