Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#65400 |
| Fitting | C23×C5×C8 ⋊ C2 |
| Sylow | C5 ⋊ C2×#435 |
564 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
184 conjugacy classes — view the full character table.
| maximal subgroup of | #11989853, #11989855, #11992199, … |
| maximal normal subgroup of | #11989853, #11989855, #11992199, … |
| maximal quotient of | C2×#10601634, C2×#10601726, C2×#10601635, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17546);