Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #1357 |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|a^2=d,c^2=f,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=defg,e^b=eg67 conjugacy classes — view the full character table.
| maximal subgroup of | #11987115, #11987116, #11987118, … |
| maximal normal subgroup of | #11987115, #11987116, #11987118, … |
| maximal quotient of | #11986021, #11986031, #11986036, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 364);