Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C5×#568 ⋊ C2 |
| Sylow | C5 ⋊ #3573 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C24×D5 |
| commutator, socle | C2×C5 | C24×C4 |
| Fitting | C5×#568 | C2 |
| prime radical | #66283 | C2 |
| cosocle | C4×C5 | C25 |
| hypercenter | #568 | D5 |
| hypocenter | C5 | #3573 |
| LCS | G ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C4 ◁ #568 | |
1424 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=f,f^2=g,h^a=h^4,e^b=eg,h^b=h^4,d^c=dg136 conjugacy classes — view the full character table.
| maximal subgroup of | #12105259, #12105261, #12105265, … |
| maximal normal subgroup of | #12105259, #12105261, #12105265, … |
| maximal quotient of | #12962722, #12962723, #12962724, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21149);