Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #1035 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C43 |
| direct product | C42×#1035 |
| Fitting | C42×C25 ⋊ C4 |
| derived, Sylow | C25 ⋊ C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | #1035 |
| commutator, hypocenter | C25 | C43 |
| Frattini, socle | C22×C5 | C22×AGL(1,𝔽5) |
| Fitting | C42×C25 | C4 |
| prime radical, cosocle | C22×D25 | C23 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C42 | |
387 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #127×#1035, C42×AGL(1,ℤ/25), #104×#1035 |
| maximal normal subgroup of | #127×#1035, C42×AGL(1,ℤ/25), #104×#1035 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 1026);