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×C22⋊C4 ⋊ C2 |
| Sylow | C5 ⋊ #2367 |
632 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=g,b^2=g,c^2=ef,d^2=e,b^a=be,c^a=cf,h^a=h^4,d^b=de,h^d=h^4130 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#2367, C2×#10605203, #12258917, … |
| maximal normal subgroup of | D5×#2367, C2×#10605203, #12258917, … |
| maximal quotient of | #12020747, #12020840, #12020867, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 7285);