Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#66091 |
| Fitting | C22×C5×D8 ⋊ C2 |
| Sylow | C5 ⋊ C2×#576 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D5 |
| commutator, cosocle | C4×C5 | C25 |
| Frattini | C4 | C24×D5 |
| Fitting | C22×C5×D8 | C2 |
| socle | C22×C5 | C22×D4 |
| hypercenter | C22×D8 | D5 |
| hypocenter | C5 | C2×#576 |
| LCS | G ▷ C4×C5 ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ C22×D8 | |
1512 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | #12014984, #12014996, #12015023, … |
| maximal normal subgroup of | #12014984, #12014996, #12015023, … |
| maximal quotient of | C2×#10610473, C2×#10610877, C2×#10611318, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21155);