Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×C5×C4⋊C4 ⋊ C2 |
| Sylow | C5 ⋊ #2274 |
696 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=f,b^2=g,c^2=e,b^a=be,d^a=de,c^b=ce,h^d=h^4148 conjugacy classes — view the full character table.
| maximal subgroup of | #12097097, #12097099, #12097101, … |
| maximal normal subgroup of | #12097097, #12097099, #12097101, … |
| maximal quotient of | #12020381, #12020384, #12020385, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 7563);