Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #1035 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C24×#1035 |
| unambiguous semidirect product | D25⋊(C23×C4) |
| Fitting | C24×C25 ⋊ C4 |
| derived, Sylow | C25 ⋊ C24×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | #1035 |
| commutator, hypocenter | C25 | C24×C4 |
| Frattini | C5 | C24×AGL(1,𝔽5) |
| Fitting | C24×C25 | C4 |
| socle | C24×C5 | AGL(1,𝔽5) |
| prime radical | C24×D25 | C2 |
| cosocle | D25 | C25 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C24 | |
2043 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #120×#1035, C24×AGL(1,ℤ/25) |
| maximal normal subgroup of | #120×#1035, C24×AGL(1,ℤ/25) |
| maximal quotient of | H(5,𝔽2)×#1035 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5603);