Finite Group DatabasebetaFinite Group Databasebeta| order | 1752 |
| isoclinism | isoclinic class of #10596842⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #10596842⋊C3 |
| Fitting, socle, derived, Sylow | C73 ⋊ C3×C8 |
| Hall | #10596842 ⋊ C3 |
| Hall | C73⋊C3 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C73 | C3×C8 |
| prime radical | D73⋊C3 | C4 |
| cosocle | #64408 | C2×C3 |
| LCS | G ▷ C73 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 73 |
| transitive degree | μt(G) = 73 |
Polycyclic presentation:
2,3,2^2,73|a^2=c,c^2=d,e^a=e^63,e^b=e^64,e^c=e^27,e^d=e^7227 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽73), C2×#10596842⋊C3, C3×#10596842⋊C3, … |
| maximal normal subgroup of | AGL(1,𝔽73), C2×#10596842⋊C3, C3×#10596842⋊C3 |
| maximal quotient of | C2×#10596842⋊C3, C3×#10596842⋊C3, #72276484 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1752, 45);