Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of D25⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×#6014⋊C5 |
| unambiguous semidirect product | (C2×#6014)⋊C5 |
| derived | C25 ⋊ C2×C5×C8 |
| Sylow | 5−1+2 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D25⋊C5 |
| commutator, hypocenter | C25 | C2×C5×C8 |
| Frattini | C4×C5 | C2×C5×D5 |
| Fitting | C2×C4×5−1+2 | C2 |
| socle | C22×C5 | C5×Dic5 |
| prime radical | C22×C52 | Dic5 |
| cosocle | C4×C25 | C22×C5 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C2×C4 | |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
176 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 152);