Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C4×#4144 |
| Fitting | C2×C4×C5×D4 ⋊ C2 |
| Sylow | C5 ⋊ C4×H(5,𝔽2) |
1660 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
148 conjugacy classes — view the full character table.
| maximal subgroup of | #11990691, #11990692, #11990698, … |
| maximal normal subgroup of | #11990691, #11990692, #11990698, … |
| maximal quotient of | C4×#65820, C4×#65879, C4×#66132, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19733);