Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D5×#401 |
| Fitting | C5×#401 ⋊ C2 |
| Sylow | C5 ⋊ C2×#401 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D5 |
| commutator, socle, cosocle | C23×C5 | C24 |
| Fitting | C5×#401 | C2 |
| prime radical | C23×D5 | C23 |
| hypercenter | #401 | D5 |
| hypocenter | C5 | C2×#401 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ #401 | |
516 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D5×#401, D5×#2401, D5×#2643, … |
| maximal normal subgroup of | C2×D5×#401, D5×#2401, D5×#2643, … |
| maximal quotient of | D5×#1443, #12021162, Dic5×#401, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12242);