Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C5 ⋊ #2378 |
464 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 213 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,d^2=e,b^a=be,c^a=cf,d^a=def,h^a=h^4,c^b=cef,d^b=de94 conjugacy classes — view the full character table.
| maximal subgroup of | #11996326, #11996330, #11996340, … |
| maximal normal subgroup of | #11996326, #11996330, #11996340, … |
| maximal quotient of | #12020921, #12020931, #12020945, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 16563);