Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #3152 |
552 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=g,b^2=e,c^2=f,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^4,d^b=dg,h^b=h^488 conjugacy classes — view the full character table.
| maximal subgroup of | #11996815, #11996817, #11996856, … |
| maximal normal subgroup of | #11996815, #11996817, #11996856, … |
| maximal quotient of | #12087156, #12087200, #12087239, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17101);