Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of AGL(1,𝔽5)×#1035 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | AGL(1,𝔽5)×#1035 |
| Fitting, derived, Sylow | C5×C25 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C5×C25 | C42 |
| Frattini | C5 | AGL(1,𝔽5)2 |
| socle | C52 | C4×AGL(1,𝔽5) |
| prime radical, cosocle | D5×D25 | C22 |
| LCS | G ▷ C5×C25 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 100 |
50 conjugacy classes — view the full character table.
| maximal subgroup of | #10352, AGL(1,𝔽5)×AGL(1,ℤ/25) |
| maximal normal subgroup of | AGL(1,𝔽5)×AGL(1,ℤ/25) |
| maximal quotient of | #10352 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 472);