Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C214 |
No aliases for this group.
| Fitting | C5×#585 ⋊ C4 |
| Sylow | C5 ⋊ #62654 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C25×AGL(1,𝔽5) |
| commutator, socle | C2×C5 | C25×C4 |
| Fitting | C5×#585 | C4 |
| prime radical | D5×#585 | C2 |
| cosocle | C2×D5 | C26 |
| hypercenter | #585 | AGL(1,𝔽5) |
| hypocenter | C5 | #62654 |
| LCS | G ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C2 ◁ #585 | |
11222 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=h,f^2=g,b^a=bg,f^a=fg,i^a=i^2,e^b=eg,d^c=dg,i^h=i^4164 conjugacy classes — view the full character table.
| maximal subgroup of | #72221904, AGL(1,𝔽5)×H(7,𝔽2), #72269816, … |
| maximal normal subgroup of | #72221904, AGL(1,𝔽5)×H(7,𝔽2), #72269816, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1116289);