Finite Group DatabasebetaFinite Group Databasebeta| order | 1000 |
| isoclinism | isoclinic class of D5×D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | D5×Dic25 |
| derived, Sylow | C5×C25 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D5×D25 |
| commutator, hypocenter | C5×C25 | C2×C4 |
| Frattini | C2×C5 | D52 |
| Fitting, cosocle | C2×C5×C25 | C22 |
| socle | C2×C52 | C2×D5 |
| prime radical | C2×C5×D5 | D5 |
| LCS | G ▷ C5×C25 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 200 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×Dic25, #14522277, D5×#6016, … |
| maximal normal subgroup of | AGL(1,𝔽5)×Dic25, #14522277, D5×#6016, … |
| maximal quotient of | D5×#6014, #14522119, Dic5×Dic25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1000, 39);