Finite Group DatabasebetaFinite Group Databasebeta| order | 1752 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D292 |
| unambiguous semidirect product | C4⋊(C3×D73) |
| Fitting | C3×C4×C73 ⋊ C2 |
| Hall | C3×C73 ⋊ D4 |
| Sylow | C73 ⋊ C3×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3 | C2×D73 |
| commutator, cosocle | C2×C73 | C22×C3 |
| Frattini | C2 | C2×C3×D73 |
| Fitting | C3×C4×C73 | C2 |
| socle | C2×C3×C73 | C22 |
| hypercenter | C3×C4 | D73 |
| hypocenter | C73 | C3×D4 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C3 ◁ C3×C4 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 876 |
447 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1752, 29);