Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| isoclinism | isoclinic class of AGL(1,𝔽25) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C8 · Schur multiplier (H2) = C3 |
| direct product | C3×AGL(1,𝔽25) |
| unambiguous semidirect product | #6053⋊C32 |
| unambiguous semidirect product | (C3×#6053)⋊C3 |
| Fitting, socle | C3×C52 ⋊ C3×C8 |
| derived, Sylow | C52 ⋊ C32×C8 |
| Hall | C3×C52⋊C3 ⋊ C8 |
| Hall | #6053 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | AGL(1,𝔽25) |
| commutator, hypocenter | C52 | C32×C8 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52 | C3×C8 |
| prime radical | C3×(C5⋊D5)⋊C3 | C4 |
| cosocle | #1043 | C2×C32 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C3 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 75 |
75 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×AGL(1,𝔽25), C3×AΓL(1,𝔽25), #72276706, … |
| maximal normal subgroup of | C2×C3×AGL(1,𝔽25), C3×AΓL(1,𝔽25), #72276706, … |
| maximal quotient of | C2×C3×AGL(1,𝔽25) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 566);