Finite Group DatabasebetaFinite Group Databasebeta| order | 1746 |
| isoclinism | isoclinic class of C3⋊(D97⋊C3) |
| automorphism | Aut(G) = D3×AGL(1,𝔽97) (order 55872) · Inn(G) = G · Out(G) = C32 |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(D97⋊C3) |
| unambiguous semidirect product | (C97⋊C3)⋊D3 |
| unambiguous semidirect product | D291⋊C3 |
| Fitting, socle, derived | C3×C97 ⋊ C2×C3 |
| Hall | C3×C97⋊C3 ⋊ C2 |
| Sylow | C97 ⋊ C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C97 | C2×C3 |
| LCS | G ▷ C3×C97 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 100 |
| transitive degree | μt(G) = 291 |
Polycyclic presentation:
2,3^2,97|c^a=c^2,d^a=d^96,d^b=d^3557 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1746, 9);