Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of D3×D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#10597028 |
| derived, Hall | C3×C25 ⋊ C22×C4 |
| Sylow | C25 ⋊ C2×C4×D3 |
| Sylow | C3 ⋊ C2×C4×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×D25 |
| commutator, hypocenter | C3×C25 | C22×C4 |
| Frattini | C2×C5 | C2×D3×D5 |
| Fitting | C22×C3×C25 | C22 |
| socle | C22×C3×C5 | C2×D5 |
| prime radical | C22×D75 | C2 |
| cosocle | C2×C3×C25 | C23 |
| LCS | G ▷ C3×C25 | |
| UCS | C1 ◁ C22 | |
162 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, 137);