Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of C9⋊D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C9 |
| direct product | C9×C9⋊D9 |
| Fitting, Sylow | C93 ⋊ C2 |
| derived | C92 ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | C9⋊D9 |
| commutator, hypocenter | C92 | C2×C9 |
| Frattini, socle | C33 | C3×C3⋊D3 |
| Fitting | C93 | C2 |
| prime radical | C3×C9⋊D9 | C3 |
| cosocle | C3×C92 | C2×C3 |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C9 | |
326 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
378 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×#92314, 3−1+2×C9⋊D9, #72243157, … |
| maximal normal subgroup of | C9×#92314, 3−1+2×C9⋊D9, #72243157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 671);