Finite Group DatabasebetaFinite Group Databasebeta| order | 1752 |
| isoclinism | isoclinic class of D73⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D73⋊A4 |
| unambiguous semidirect product | (C22⋊(C73⋊C3))⋊C2 |
| Fitting, socle, derived | C22×C73 ⋊ C2×C3 |
| Hall | C22×D73 ⋊ C3 |
| Sylow | C73 ⋊ C2×A4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C73 | C2×C3 |
| LCS | G ▷ C22×C73 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 292 |
Polycyclic presentation:
2,3,2^2,73|e^a=e^72,c^b=cd,d^b=c,e^b=e^6456 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1752, 54);