Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | D4×C22⋊Dic5 |
| Sylow | C5 ⋊ D4×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D5 |
| commutator | C22×C5 | C23×C4 |
| Fitting, prime radical | C23×C5×D4 | C2 |
| socle, cosocle | C23×C5 | C24 |
| hypercenter | C23×D4 | D5 |
| hypocenter | C5 | D4×C22⋊C4 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ C23×D4 | |
1252 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
130 conjugacy classes — view the full character table.
| maximal subgroup of | #11995717, #11995721, #11995745, … |
| maximal normal subgroup of | #11995717, #11995721, #11995745, … |
| maximal quotient of | C22⋊C4×C22⋊Dic5, C4⋊C4×C22⋊Dic5, D4×#3963, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17858);