Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C5×#1657 ⋊ C2 |
| Sylow | C5 ⋊ #18990 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D5×#120 |
| commutator, cosocle | C42×C5 | C24 |
| Frattini | C42 | C23×D5 |
| Fitting | C5×#1657 | C2 |
| socle | C22×C5 | C2×#120 |
| hypercenter | #1657 | D5 |
| hypocenter | C5 | #18990 |
| LCS | G ▷ C42×C5 ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #1657 | |
862 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^8,5|b^2=h,d^2=g,e^2=g,f^2=gh,b^a=be,c^a=cf,e^a=eg,f^a=fgh,e^b=eg,f^b=fh,i^b=i^4,e^c=eh,f^c=fgh,i^d=i^480 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 150765);