Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#66169 |
| Fitting | C2×C5×H(5,𝔽2) ⋊ C2 |
| Sylow | C5 ⋊ C2×#576 |
1512 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #12115199, #12115202, #12115226, … |
| maximal normal subgroup of | #12115199, #12115202, #12115226, … |
| maximal quotient of | C2×#10614294, C2×#10615830, C2×#10614293, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21259);