Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×C5×C4⋊C4 ⋊ C4 |
| Sylow | C5 ⋊ #2345 |
548 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=g,b^2=ef,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 | #13019968, #13019969, #13019976, … |
| maximal normal subgroup of | #13019968, #13019969, #13019976, … |
| maximal quotient of | C4⋊C4×C22⋊AGL(1,𝔽5), #13028002, #13028021, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19186);