Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of C3⋊(D27⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C32 |
| direct product | C3×C3⋊(D27⋊C3) |
| unambiguous semidirect product | C3⋊(C3×D27⋊C3) |
| Fitting, Sylow | C32×C27⋊C3 ⋊ C2 |
| derived | C3×C27 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊(D27⋊C3) |
| commutator, cosocle, hypocenter | C3×C27 | C2×C32 |
| Frattini | C9 | C32×C3⋊D3 |
| Fitting | C32×C27⋊C3 | C2 |
| socle | C33 | C3×D9 |
| LCS | G ▷ C3×C27 | |
| UCS | C1 ◁ C3 | |
362 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 74 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 | #72243564, C3×D3×D27⋊C3, D3×C3⋊(D27⋊C3), … |
| maximal normal subgroup of | #72243564, C3×D3×D27⋊C3, D3×C3⋊(D27⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1633);