Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C28 |
| direct product | C2×#65509 |
| Sylow | C5 ⋊ C2×#386 |
1576 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | #12004643, #12004645, #12005765, … |
| maximal normal subgroup of | #12004643, #12004645, #12005765, … |
| maximal quotient of | C2×#10602337, C2×#10602357, C2×#10602338, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17854);