Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#65678 |
| Sylow | C5 ⋊ C2×#431 |
528 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 234 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #13015272, #13015278, #13015282, … |
| maximal normal subgroup of | #13015272, #13015278, #13015282, … |
| maximal quotient of | C2×#10604173, C2×C4×#4003, C2×C4×#4004, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19113);