Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C5×Q8⋊C8 ⋊ C2 |
| Sylow | C5 ⋊ #1588 |
166 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 63 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,b^2=f,c^2=ef,d^2=f,e^2=g,b^a=bd,c^a=cfg,d^a=df,d^b=df,h^c=h^494 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1588, C2×#10599016, #12068868, … |
| maximal normal subgroup of | D5×#1588, C2×#10599016, #12068868, … |
| maximal quotient of | #11990116, #11990161, #11990570, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 1098);