Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×C5×Q16 ⋊ C2 |
| Sylow | C5 ⋊ #2950 |
456 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=f,b^2=g,c^2=fg,e^2=g,b^a=be,d^a=dg,e^a=eg,e^b=eg,d^c=dg,h^d=h^4100 conjugacy classes — view the full character table.
| maximal subgroup of | #12252646, #12252648, #12252650, … |
| maximal normal subgroup of | #12252646, #12252648, #12252650, … |
| maximal quotient of | #12068769, #12068993, #12069140, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 13533);