Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of D3×D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×D3×D25 |
| unambiguous semidirect product | (D3×C25)⋊C23 |
| unambiguous semidirect product | (C3×D25)⋊C23 |
| unambiguous semidirect product | D75⋊C23 |
| Fitting | C22×C3×C25 ⋊ C22 |
| derived, Hall | C3×C25 ⋊ C24 |
| Sylow | C25 ⋊ C23×D3 |
| Sylow | C3 ⋊ C23×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×D25 |
| commutator, cosocle, hypocenter | C3×C25 | C24 |
| Frattini | C5 | C22×D3×D5 |
| Fitting | C22×C3×C25 | C22 |
| socle | C22×C3×C5 | C2×D5 |
| LCS | G ▷ C3×C25 | |
| UCS | C1 ◁ C22 | |
402 conjugacy classes of subgroups.
| transitive degree | μt(G) = 300 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 203);