Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C5 · Schur multiplier (H2) = C210 |
| direct product | C24×C5×AGL(1,𝔽5) |
| unambiguous semidirect product | D5⋊(C23×C4×C5) |
| Fitting, socle | C24×C52 ⋊ C4 |
| derived | C5 ⋊ C24×C4×C5 |
| Sylow | C52 ⋊ C24×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C5 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C24×C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C24×C52 | C4 |
| prime radical | C24×C5×D5 | C2 |
| cosocle | D5 | C25×C5 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C24×C5 | |
2791 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×AGL(1,𝔽5)×#120, C24×AGL(1,ℤ/25) |
| maximal normal subgroup of | C5×AGL(1,𝔽5)×#120 |
| maximal quotient of | C24×AGL(1,ℤ/25), C5×AGL(1,𝔽5)×H(5,𝔽2) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 10274);