Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C2 |
| direct product | C2×#64665 |
| derived, Sylow | C5 ⋊ C2×C64 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C2×C64 |
| Frattini | C16 | C2×AGL(1,𝔽5) |
| Fitting | C2×C5×C16 | C4 |
| socle, prime radical | C22×C5 | C32 |
| cosocle | #3926 | C22 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C2×C16 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#64665, #13014518, #13014520, … |
| maximal normal subgroup of | C4×#64665, #13014518, #13014520, … |
| maximal quotient of | C4×#64665, C22⋊#64665, C4⋊#64665, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 715);