Finite Group DatabasebetaFinite Group Databasebeta| order | 1000 |
| isoclinism | isoclinic class of D25⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C4×D25⋊C5 |
| unambiguous semidirect product | (C4×D25)⋊C5 |
| Fitting | C4×5−1+2 ⋊ C2 |
| derived | C25 ⋊ C2×C4×C5 |
| Sylow | 5−1+2 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D25⋊C5 |
| commutator, hypocenter | C25 | C2×C4×C5 |
| Frattini, socle | C2×C5 | C2×C5×D5 |
| Fitting | C4×5−1+2 | C2 |
| prime radical | C2×D25⋊C5 | C2 |
| cosocle | C2×C25 | C22×C5 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C4 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 100 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | C8×D25⋊C5, #87712⋊C5, (D25⋊C5)⋊C8, … |
| maximal normal subgroup of | C8×D25⋊C5, #87712⋊C5, (D25⋊C5)⋊C8, … |
| maximal quotient of | C8×D25⋊C5, #87712⋊C5, C4×Dic25⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1000, 57);