Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of D25⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C5 · Schur multiplier (H2) = C4 |
| direct product | C4×Dic25⋊C5 |
| unambiguous semidirect product | (C4×Dic25)⋊C5 |
| derived | C25 ⋊ C42×C5 |
| Sylow | 5−1+2 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D25⋊C5 |
| commutator, hypocenter | C25 | C42×C5 |
| Frattini, socle | C22×C5 | C2×C5×D5 |
| Fitting | C2×C4×5−1+2 | C2 |
| prime radical | C22×C52 | C2×D5 |
| cosocle | C22×C25 | C22×C5 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C2×C4 | |
106 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | C42×D25⋊C5, #72275624, #72275800, … |
| maximal normal subgroup of | C42×D25⋊C5, #72275624, #72275800, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 154);