Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×Q8⋊C8 ⋊ C2 |
| Sylow | C5 ⋊ #1489 |
266 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 73 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=e,d^2=f,e^2=g,b^a=bd,c^a=cg,d^a=df,c^b=cf,d^b=df,h^b=h^4,h^c=h^494 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1489, C2×#10599031, #12065731, … |
| maximal normal subgroup of | D5×#1489, C2×#10599031, #12065731, … |
| maximal quotient of | #11987457, #11987462, #11987467, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 1113);