Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C4 |
No aliases for this group.
| Fitting | C2×C5×#121 ⋊ C4 |
| Sylow | C5 ⋊ #20912 |
2278 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^8,5|a^2=g,b^2=egh,d^2=h,e^2=h,g^2=h,b^a=be,c^a=cf,d^a=dh,i^a=i^3,e^b=eh,g^b=gh,i^b=i^2,i^g=i^492 conjugacy classes — view the full character table.
| maximal subgroup of | #72258359, AGL(1,𝔽5)×#3006 |
| maximal normal subgroup of | #72258359, AGL(1,𝔽5)×#3006 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1105159);