Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of C3⋊((C3⋊D3)⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C35 |
| direct product | C32×C3⋊((C3⋊D3)⋊C3) |
| unambiguous semidirect product | C3⋊(C32×(C3⋊D3)⋊C3) |
| Fitting, Sylow | C33×H(3,𝔽3) ⋊ C2 |
| derived | C33 ⋊ C2×C33 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C3⋊((C3⋊D3)⋊C3) |
| commutator, cosocle, hypocenter | C33 | C2×C33 |
| Frattini | C3 | C33×C3⋊D3 |
| Fitting | C33×H(3,𝔽3) | C2 |
| socle | C34 | C3×D3 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C32 | |
3410 conjugacy classes of subgroups; only the 220 normal subgroups are shown.
This group has 3410 conjugacy classes of subgroups — too many to draw. Only its 220 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
189 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#13091503, C3×#13091647, #72221909, … |
| maximal normal subgroup of | C3⋊D3×C3⋊((C3⋊D3)⋊C3), C3×#11758090, C3×#11758084, … |
| maximal quotient of | #72221880, C3×#13091503, #72221892, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1756);