Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C42 · Schur multiplier (H2) = C214×C4 |
| direct product | C24×C4×AGL(1,𝔽5) |
| unambiguous semidirect product | D5⋊(C23×C42) |
| Fitting | C24×C4×C5 ⋊ C4 |
| derived, Sylow | C5 ⋊ C24×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C4 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C24×C42 |
| Frattini | C2 | C25×AGL(1,𝔽5) |
| Fitting | C24×C4×C5 | C4 |
| socle | C25×C5 | C2×C4 |
| prime radical | C25×D5 | C22 |
| cosocle | C2×D5 | C26 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C24×C4 | |
24030 conjugacy classes of subgroups; only the 12696 normal subgroups are shown.
This group has 24030 conjugacy classes of subgroups — too many to draw. Only its 12696 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
320 conjugacy classes. The character table is too large to display.
| maximal quotient of | C2×AGL(1,𝔽5)×#568, C2×C4×#41×AGL(1,𝔽5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1116273);