Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C34 |
| unambiguous semidirect product | C3⋊#92338 |
| Fitting, derived, Sylow | C3×C32⋊H(3,𝔽3) ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C32 | C3⋊(C3⋊(C3⋊D3)) |
| commutator, Fitting, cosocle, hypocenter | C3×C32⋊H(3,𝔽3) | C2 |
| socle | C33 | C3⋊(C3⋊D3) |
| LCS | G ▷ C3×C32⋊H(3,𝔽3) | |
| UCS | C1 ◁ C32 | |
1934 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
Polycyclic presentation:
2,3^6|b^a=b^2,c^a=c^2,d^a=d^2,e^a=e^2,c^b=cf,d^b=dg90 conjugacy classes — view the full character table.
| maximal subgroup of | #72214065, D3×#92338, #72214468, … |
| maximal normal subgroup of | #72214065, D3×#92338, #72214468, … |
| maximal quotient of | C3×C3⋊#92338, #72254101, #72277572 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1471);