Finite Group DatabasebetaFinite Group Databasebeta| order | 1752 |
| isoclinism | isoclinic class of #64408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×#64408 |
| Fitting, socle | C2×C3×C73 ⋊ C4 |
| derived, Sylow | C73 ⋊ C2×C3×C4 |
| Hall | C3×C73 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #64408 |
| commutator, hypocenter | C73 | C2×C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C73 | C4 |
| prime radical | C2×C3×D73 | C2 |
| cosocle | D73 | C22×C3 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C2×C3 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 438 |
132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1752, 55);