Finite Group DatabasebetaFinite Group Databasebeta| order | 1752 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C73 · Schur multiplier (H2) = C2 |
| direct product | C2×A4×C73 |
| unambiguous semidirect product | C23⋊(C3×C73) |
| Fitting, socle, Hall | C23×C73 ⋊ C3 |
| derived | C22 ⋊ C2×C3×C73 |
| Sylow | C23 ⋊ C3×C73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C73 | A4 |
| commutator, cosocle, hypocenter | C22 | C2×C3×C73 |
| Frattini | C1 | G |
| Fitting, socle | C23×C73 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C2×C73 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 438 |
584 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1752, 59);