Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C5×#104 ⋊ C2 |
| Sylow | C5 ⋊ #2007 |
370 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 370 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) = 160 |
Polycyclic presentation:
2^7,5|a^2=g,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^4,c^b=cf,d^b=dg,h^b=h^4,e^c=eg82 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#2007, C2×#10601186, #12126263, … |
| maximal normal subgroup of | D5×#2007, C2×#10601186, #12126263, … |
| maximal quotient of | #11999637, #11999638, #11999644, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 3268);