Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C4 |
No aliases for this group.
| Fitting | C2×C5×#376 ⋊ C2 |
| Sylow | C5 ⋊ #34641 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C23×D5 |
| commutator, socle, cosocle | C23×C5 | C25 |
| Frattini | C23 | C24×D5 |
| Fitting | C2×C5×#376 | C2 |
| hypercenter | C2×#376 | D5 |
| hypocenter | C5 | #34641 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C22×C4 ◁ C2×#376 | |
3694 conjugacy classes of subgroups; only the 827 normal subgroups are shown.
This group has 3694 conjugacy classes of subgroups — too many to draw. Only its 827 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|b^2=f,c^2=g,e^2=h,b^a=bf,c^a=cg,d^a=dh,i^a=i^4,c^b=ch224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 336943);