Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D5×#548 |
| Fitting | C5×#548 ⋊ C2 |
| Sylow | C5 ⋊ C2×#548 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D5 |
| commutator, socle, cosocle | C22×C5 | C25 |
| Fitting | C5×#548 | C2 |
| hypercenter | #548 | D5 |
| hypocenter | C5 | C2×#548 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ #548 | |
1620 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3265, D5×#3269, D5×#3270, … |
| maximal normal subgroup of | D5×#3265, D5×#3269, D5×#3270, … |
| maximal quotient of | Q8×D5×C22⋊C4, D5×#2341, D5×#2351, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 20717);