Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C4×#4094 |
| Sylow | C5 ⋊ C4×#131 |
572 conjugacy classes of subgroups; only the 381 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 381 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #11989974, #11989979, #11989985, … |
| maximal normal subgroup of | #11989974, #11989979, #11989985, … |
| maximal quotient of | C8×#4094, #12064912, #12064965, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 16323);