Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Fitting | C23×C5×D4 ⋊ C4 |
| Sylow | C5 ⋊ #20598 |
5982 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=g,e^2=h,b^a=be,c^a=cf,d^a=dh,e^a=eh,i^a=i^2,e^b=eh,i^g=i^4104 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#3003, #72221394, #72221450, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#3003, #72221394, #72221450 |
| maximal quotient of | #72226429 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1104441);