Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C5×M64 ⋊ C2 |
| Sylow | C5 ⋊ #1419 |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=d,c^2=efg,d^2=g,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^4,c^b=ceg,d^b=dg,e^b=ef,f^b=fg,h^b=h^4106 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1419, C2×#10598095, #12019775, … |
| maximal normal subgroup of | D5×#1419, C2×#10598095, #12019775, … |
| maximal quotient of | #11986757, #11986862, #11986934, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 177);