Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C5×#2021 ⋊ C2 |
| Sylow | C5 ⋊ #24262 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D5×#120 |
| commutator, cosocle | C24×C5 | C24 |
| Frattini | C24 | C23×D5 |
| Fitting | C5×#2021 | C2 |
| socle | C22×C5 | C2×#120 |
| hypercenter | #2021 | D5 |
| hypocenter | C5 | #24262 |
| LCS | G ▷ C24×C5 ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ #2021 | |
1654 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^8,5|b^2=e,d^2=e,b^a=be,c^a=cf,d^a=de,g^a=gh,c^b=cg,f^b=fh,d^c=dh,i^d=i^492 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 205216);