Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C5 ⋊ #1411 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=d,b^2=g,c^2=fg,d^2=g,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^4,c^b=cfg,d^b=def,e^b=eg,d^c=dfg,e^d=eg61 conjugacy classes — view the full character table.
| maximal subgroup of | #11987134, #11987135, #11987137, … |
| maximal normal subgroup of | #11987134, #11987135, #11987137, … |
| maximal quotient of | #11986685, #11986715, #11986816, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 368);