Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of D3×D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | D3×#6014 |
| derived, Hall | C3×C25 ⋊ C2×C8 |
| Sylow | C25 ⋊ D3×C8 |
| Sylow | C3 ⋊ C2×#6014 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D3×D25 |
| commutator, hypocenter | C3×C25 | C2×C8 |
| Frattini | C4×C5 | D3×D5 |
| Fitting, cosocle | C3×C4×C25 | C22 |
| socle | C2×C3×C5 | C2×Dic5 |
| prime radical | C2×C5×D3 | Dic5 |
| LCS | G ▷ C3×C25 | |
| UCS | C1 ◁ C4 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 600 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 15);