Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×C5×D4 ⋊ C4 |
| Sylow | C5 ⋊ #2354 |
632 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=g,b^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,h^a=h^2,d^b=de,h^g=h^470 conjugacy classes — view the full character table.
| maximal subgroup of | #13018975, #13018979, #13018983, … |
| maximal normal subgroup of | #13018975, #13018979, #13018983, … |
| maximal quotient of | #13027999, C4⋊C4×C4⋊AGL(1,𝔽5), #13028019, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19263);