Finite Group DatabasebetaFinite Group Databasebeta| order | 1752 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| direct product | Q8×C73⋊C3 |
| Fitting, Hall | Q8×C73 ⋊ C3 |
| Sylow | C73 ⋊ C3×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×C73⋊C3 |
| commutator, socle, cosocle | C2×C73 | C22×C3 |
| Fitting | Q8×C73 | C3 |
| prime radical | C2×C73⋊C3 | C22 |
| hypercenter | Q8 | C73⋊C3 |
| hypocenter | C73 | C3×Q8 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 584 |
135 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1752, 24);