Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C2×C5×#95 ⋊ C2 |
| Sylow | C5 ⋊ #1437 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C22×D5 |
| commutator | C22×C5 | C2×C42 |
| Fitting | C2×C5×#95 | C2 |
| socle, cosocle | C24×C5 | C23 |
| prime radical | C24×D5 | C22 |
| hypercenter | C2×#95 | D5 |
| hypocenter | C5 | #1437 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C24 ◁ C2×#95 | |
828 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=f,b^2=g,c^2=ef,b^a=bd,c^a=ce,h^a=h^4,h^b=h^4136 conjugacy classes — view the full character table.
| maximal subgroup of | #11990809, D5×#1437, C2×#10600201, … |
| maximal normal subgroup of | #11990809, D5×#1437, C2×#10600201, … |
| maximal quotient of | #11987219, #11987221, #11987225, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2283);