Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C2×C43 |
No aliases for this group.
| Fitting | C5×#382 ⋊ C4 |
| Sylow | C5 ⋊ #14168 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×AGL(1,𝔽5) |
| commutator, socle | C23×C5 | C23×C4 |
| Fitting | C5×#382 | C4 |
| prime radical, cosocle | C23×D5 | C24 |
| hypercenter | #382 | AGL(1,𝔽5) |
| hypocenter | C5 | #14168 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ #382 | |
1342 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 1342 conjugacy classes of subgroups — too many to draw. Only its 288 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=h,b^2=eg,c^2=h,d^2=g,b^a=be,c^a=cf,d^a=de,i^a=i^3,c^b=cg,i^c=i^2,i^h=i^4104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1098663);