Finite Group DatabasebetaFinite Group Databasebeta| order | 1752 |
| isoclinism | isoclinic class of #10596842 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C1 |
| direct product | C3×#10596842 |
| Fitting, socle, Hall | C3×C73 ⋊ C8 |
| derived, Sylow | C73 ⋊ C3×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #10596842 |
| commutator, hypocenter | C73 | C3×C8 |
| Frattini | C1 | G |
| Fitting, socle | C3×C73 | C8 |
| prime radical | C3×D73 | C4 |
| cosocle | #64408 | C2×C3 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 76 |
| transitive degree | μt(G) = 219 |
51 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10596842⋊C3, D3×#10596842 |
| maximal normal subgroup of | C3×#10596842⋊C3, D3×#10596842 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1752, 47);