Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C33 |
| direct product | D3×#6908 |
| unambiguous semidirect product | C3⋊(C2×#6908) |
| Fitting, Sylow | C3×#6908 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center | C9 | D3×H(3,𝔽3) |
| commutator, cosocle | C33 | C2×C33 |
| Frattini | C32 | C33×D3 |
| Fitting | C3×#6908 | C2 |
| socle | C32 | C2×C3×H(3,𝔽3) |
| hypercenter | #6908 | D3 |
| hypocenter | C3 | C2×#6908 |
| LCS | G ▷ C33 ▷ C32 ▷ C3 | |
| UCS | C1 ◁ C9 ◁ C3×C9 ◁ #6908 | |
467 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 467 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
153 conjugacy classes — view the full character table.
| maximal subgroup of | #72243619, D3×#10624934, #72243714, … |
| maximal normal subgroup of | D3×#10624934, D3×#92280, D3×#92344, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1680);