Finite Group DatabasebetaFinite Group Databasebeta| order | 1752 |
| isoclinism | isoclinic class of D219 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C4×D219 |
| Fitting | C3×C4×C73 ⋊ C2 |
| derived, Hall | C3×C73 ⋊ C2×C4 |
| Sylow | C73 ⋊ C4×D3 |
| Sylow | C3 ⋊ C4×D73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D219 |
| commutator, hypocenter | C3×C73 | C2×C4 |
| Frattini | C2 | C2×D219 |
| Fitting | C3×C4×C73 | C2 |
| socle, cosocle | C2×C3×C73 | C22 |
| prime radical | C2×D219 | C2 |
| LCS | G ▷ C3×C73 | |
| UCS | C1 ◁ C4 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 876 |
444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1752, 38);