Finite Group DatabasebetaFinite Group Databasebeta| order | 1746 |
| isoclinism | isoclinic class of D97⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D97⋊C9 |
| unambiguous semidirect product | (C97⋊C9)⋊C2 |
| derived, Sylow | C97 ⋊ C2×C9 |
| Hall | C97⋊C9 ⋊ C2 |
| Hall | D97 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D97⋊C3 |
| commutator, hypocenter | C97 | C2×C9 |
| Fitting, socle, cosocle | C3×C97 | C2×C3 |
| prime radical | C3×D97 | C3 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 106 |
| transitive degree | μt(G) = 873 |
Polycyclic presentation:
2,3^2,97|b^3=c,d^a=d^96,d^b=d^6166 conjugacy classes — view the full character table.
| maximal subgroup of | #87604⋊C9, C2×D97⋊C9, C7×D97⋊C9, … |
| maximal normal subgroup of | #87604⋊C9, C2×D97⋊C9, C7×D97⋊C9, … |
| maximal quotient of | Dic97⋊C9, C2×D97⋊C9, C7×D97⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1746, 1);