Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C4 |
| direct product | C2×D5×#124 |
| Fitting | C2×C5×#124 ⋊ C2 |
| Sylow | C5 ⋊ C22×#124 |
1880 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #11990765, #12014787, #12014804, … |
| maximal normal subgroup of | #11990765, #12014787, #12014804, … |
| maximal quotient of | C2×D5×#382, C2×D5×#388, C2×D5×#390, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 20051);