Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of #4169 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C32 |
| direct product | C9×#4169 |
| Fitting, Sylow | C9×C32⋊C9 ⋊ C2 |
| derived | C3×C9 ⋊ C2×C3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | #4169 |
| commutator, hypocenter | C3×C9 | C2×C3×C9 |
| Frattini, socle | C33 | C32×D3 |
| Fitting | C9×C32⋊C9 | C2 |
| prime radical | C3×#4169 | C3 |
| cosocle | C32×C9 | C2×C32 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C9 | |
275 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 275 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
189 conjugacy classes — view the full character table.
| maximal subgroup of | C9×#92299, #72243275, D9×#4169, … |
| maximal normal subgroup of | #72243275, D9×#4169 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 681);