Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C42 |
No aliases for this group.
| Sylow | C5 ⋊ #14661 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D5 |
| commutator | C23×C5 | C23×C4 |
| Fitting, prime radical | C22×C5×#127 | C2 |
| socle, cosocle | C24×C5 | C24 |
| hypercenter | C22×#127 | D5 |
| hypocenter | C5 | #14661 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C24 ◁ C22×#127 | |
2502 conjugacy classes of subgroups; only the 411 normal subgroups are shown.
This group has 2502 conjugacy classes of subgroups — too many to draw. Only its 411 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^8,5|a^2=f,b^2=h,d^2=e,b^a=be,c^a=cf,c^b=cg,d^b=def,i^b=i^4,d^c=de164 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 100607);