Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#66150 |
| Fitting | C23×C5×Q8 ⋊ C2 |
| Sylow | C5 ⋊ C2×#536 |
1512 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | #12005830, #12005878, #12005893, … |
| maximal normal subgroup of | #12005830, #12005878, #12005893, … |
| maximal quotient of | C2×#10615793, C2×#10613917, C2×#10613888, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21232);