Finite Group DatabasebetaFinite Group Databasebeta| order | 1000 |
| isoclinism | isoclinic class of AGL(1,𝔽5)×D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | AGL(1,𝔽5)×D25 |
| unambiguous semidirect product | (AGL(1,𝔽5)×C25)⋊C2 |
| unambiguous semidirect product | #92533⋊C2 |
| Fitting, derived, Sylow | C5×C25 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C5×C25 | C2×C4 |
| Frattini | C5 | D5×AGL(1,𝔽5) |
| socle | C52 | C4×D5 |
| prime radical | D5×D25 | C2 |
| cosocle | D5×C25 | C22 |
| LCS | G ▷ C5×C25 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 100 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#1035, C2×AGL(1,𝔽5)×D25, D25×#1035, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#1035, C2×AGL(1,𝔽5)×D25, AGL(1,𝔽5)×D25⋊C5 |
| maximal quotient of | #170×D25, #14522273, #14522274, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1000, 87);