Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C32 |
| direct product | C3×C9⋊#272 |
| Fitting, Sylow | C3×C9×H(3,𝔽3) ⋊ C2 |
| derived | C9×H(3,𝔽3) ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C3⋊(C3⋊D9) |
| commutator, cosocle, hypocenter | C9×H(3,𝔽3) | C2×C3 |
| Frattini | C32 | C3×C3⋊(C3⋊D3) |
| Fitting | C3×C9×H(3,𝔽3) | C2 |
| socle | C33 | C3⋊(C3⋊D3) |
| LCS | G ▷ C9×H(3,𝔽3) | |
| UCS | C1 ◁ C32 | |
758 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | #72243426, C3×#13091511, #72253782, … |
| maximal normal subgroup of | C3×#13091511, #72253782, C3×((C3⋊D3)⋊C3)⋊D9, … |
| maximal quotient of | #72243534 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1437);