Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C4×C5×Q8 ⋊ C2 |
| Sylow | C5 ⋊ #2396 |
528 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,c^b=cg,h^b=h^4124 conjugacy classes — view the full character table.
| maximal subgroup of | #11994386, #11994391, #12071575, … |
| maximal normal subgroup of | #11994386, #11994391, #12071575, … |
| maximal quotient of | #12021011, #12021025, #12021047, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 16304);