Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#66100 |
| Fitting | C22×C5×Q16 ⋊ C2 |
| Sylow | C5 ⋊ C2×#578 |
1408 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | #12014989, #12015001, #12015030, … |
| maximal normal subgroup of | #12014989, #12015001, #12015030, … |
| maximal quotient of | C2×#10610521, C2×#10610877, C2×#10610505, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21164);