Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C5 ⋊ #2916 |
440 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 249 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=f,b^2=e,e^2=g,f^2=g,b^a=be,e^a=eg,h^b=h^4,d^c=dg112 conjugacy classes — view the full character table.
| maximal subgroup of | #12117817, #12117818, #12117825, … |
| maximal normal subgroup of | #12117817, #12117818, #12117825, … |
| maximal quotient of | #12068287, #12068292, #12068340, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17623);