Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28×C4 |
| direct product | C2×D5×#117 |
| Fitting | C2×C5×#117 ⋊ C2 |
| Sylow | C5 ⋊ C22×#117 |
1880 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #12004530, #12004588, #12004608, … |
| maximal normal subgroup of | #12004530, #12004588, #12004608, … |
| maximal quotient of | C2×D5×#376, C2×C4×D5×C22⋊C4, C2×C4×D5×C4⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19711);