Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #1773 |
224 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 105 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=e,b^2=f,c^2=de,d^2=g,b^a=bd,c^a=cg,d^b=dg,e^b=eg,h^c=h^4100 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1773, C2×#10599535, #12097316, … |
| maximal normal subgroup of | D5×#1773, C2×#10599535, #12097316, … |
| maximal quotient of | #11990465, #11990469, #11990473, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 1617);