Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of D75 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | C4×Dic75 |
| derived, Hall | C3×C25 ⋊ C42 |
| Sylow | C25 ⋊ C4×Dic3 |
| Sylow | C3 ⋊ C4×Dic25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D75 |
| commutator, hypocenter | C3×C25 | C42 |
| Frattini | C22×C5 | C2×D15 |
| Fitting | C2×C3×C4×C25 | C2 |
| socle, prime radical | C22×C3×C5 | C2×D5 |
| cosocle | C22×C3×C25 | C22 |
| LCS | G ▷ C3×C25 | |
| UCS | C1 ◁ C2×C4 | |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1200 |
312 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 72);