Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#65113 |
| Fitting | C2×C5×#104 ⋊ C2 |
| Sylow | C5 ⋊ C2×#443 |
472 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#65113, #12097851, #12097858, … |
| maximal normal subgroup of | C4×#65113, #12097851, #12097858, … |
| maximal quotient of | C2×#10598941, C2×#10599005, C2×#10598942, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12791);