Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×D5×M32 |
| Fitting | C2×C5×M32 ⋊ C2 |
| Sylow | C5 ⋊ C22×M32 |
400 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1375, #12014148, D5×#1376, … |
| maximal normal subgroup of | D5×#1375, #12014148, D5×#1376, … |
| maximal quotient of | C2×D5×#346, C4×D5×M32, C2×Dic5×M32, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15818);