Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C5×#2399 ⋊ C2 |
| Sylow | C5 ⋊ #34840 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C23×D5 |
| commutator, socle, cosocle | C23×C5 | C25 |
| Frattini | C23 | C24×D5 |
| Fitting | C5×#2399 | C2 |
| prime radical | C22×D20 | C23 |
| hypercenter | #2399 | D5 |
| hypocenter | C5 | #34840 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C22×C4 ◁ #2399 | |
1944 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^8,5|a^2=g,c^2=gh,e^2=f,b^a=bf,c^a=cg,c^b=ch,d^b=dh,i^b=i^4,i^d=i^4164 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 339916);