Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #1290 |
136 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 61 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=d,b^2=e,c^2=fg,d^2=f,e^2=fg,b^a=bc,c^a=cf,e^a=efg,d^b=dg,h^b=h^488 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1290, C2×#10598246, #11989193, … |
| maximal normal subgroup of | D5×#1290, C2×#10598246, #11989193, … |
| maximal quotient of | #11985837, #11985845, #11985847, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 328);