Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×C8×D4 ⋊ C2 |
| Sylow | C5 ⋊ #1580 |
192 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 192 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,c^2=ef,d^2=f,e^2=g,b^a=bd,c^a=cf,d^a=df,h^a=h^4,d^b=df124 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1580, C2×#10601633, #12068701, … |
| maximal normal subgroup of | D5×#1580, C2×#10601633, #12068701, … |
| maximal quotient of | #11990076, #11990080, #11990545, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 3715);