Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #22039 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C23×D5 |
| commutator, socle | C23×C5 | C23×C4 |
| Fitting, prime radical | C5×#2388 | C2 |
| cosocle | C22×C4×C5 | C24 |
| hypercenter | #2388 | D5 |
| hypocenter | C5 | #22039 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C22×C4 ◁ #2388 | |
1028 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^8,5|a^2=g,b^2=g,g^2=h,b^a=be,c^a=cf,d^a=deh,i^a=i^4,c^b=ce,d^b=dh,i^b=i^4,d^c=dh152 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 180690);