Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C5 ⋊ #1366 |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=d,b^2=f,c^2=fg,d^2=ef,e^2=g,b^a=bc,c^a=ce,e^a=eg,f^a=fg,h^a=h^4,c^b=cf,d^b=def,e^b=eg67 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1366, C2×#10598291, #12010666, … |
| maximal normal subgroup of | D5×#1366, C2×#10598291, #12010666, … |
| maximal quotient of | #11986126, #11986478, C2×#10598291, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 373);