Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#65795 |
| Fitting | C2×C5×#41 ⋊ C4 |
| Sylow | C5 ⋊ C2×#421 |
772 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
64 conjugacy classes — view the full character table.
| maximal subgroup of | #13021830, #13021832, #13021847, … |
| maximal normal subgroup of | #13021830, #13021832, #13021847, … |
| maximal quotient of | C2×#10604403, C2×#10604438, C2×#10605001, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19617);