Finite Group DatabasebetaFinite Group Databasebeta| order | 1752 |
| isoclinism | isoclinic class of D3×#64408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | D3×#64408 |
| unambiguous semidirect product | (C3×#64408)⋊C2 |
| unambiguous semidirect product | (C3⋊#64408)⋊C2 |
| Fitting, socle, derived, Hall | C3×C73 ⋊ C2×C4 |
| Sylow | C73 ⋊ C4×D3 |
| Sylow | C3 ⋊ C2×#64408 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C73 | C2×C4 |
| prime radical | D3×D73 | C2 |
| cosocle | C3×D73 | C22 |
| LCS | G ▷ C3×C73 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 76 |
| transitive degree | μt(G) = 219 |
66 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#10596842, D3×#64408⋊C3 |
| maximal normal subgroup of | D3×#10596842, D3×#64408⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1752, 49);