Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×D5×C22⋊Q8 |
| Fitting | C2×C5×C22⋊Q8 ⋊ C2 |
| Sylow | C5 ⋊ C22×C22⋊Q8 |
1840 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #11990743, D5×#1472, #12065389, … |
| maximal normal subgroup of | #11990743, D5×#1472, #12065389, … |
| maximal quotient of | C2×D5×#380, C2×D5×#385, C2×D5×#387, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19957);