Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D5×#398 |
| Fitting | C5×#398 ⋊ C2 |
| Sylow | C5 ⋊ C2×#398 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D5 |
| commutator, socle, cosocle | C23×C5 | C24 |
| Fitting | C5×#398 | C2 |
| prime radical | C23×D5 | C23 |
| hypercenter | #398 | D5 |
| hypocenter | C5 | C2×#398 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ #398 | |
692 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1346, #12009984, D5×#1609, … |
| maximal normal subgroup of | D5×#1346, #12009984, D5×#1609, … |
| maximal quotient of | D5×#1441, D5×#1442, D5×#1444, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 11758);