Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of C3⋊#92301 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C36 |
| unambiguous semidirect product | C3⋊#92301 |
| Fitting, Sylow | C3×C32⋊H(3,𝔽3) ⋊ C2 |
| derived | C35 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C35 | C2×C3 |
| Frattini | C32 | C3×C3⋊(C3⋊D3) |
| Fitting | C3×C32⋊H(3,𝔽3) | C2 |
| socle | C33 | C3×C3⋊D3 |
| LCS | G ▷ C35 | |
| UCS | C1 | |
2603 conjugacy classes of subgroups.
| transitive degree | μt(G) = 81 |
Polycyclic presentation:
2,3^6|c^a=c^2,d^a=d^2,e^a=e^2,f^a=f^2,g^a=g^2,c^b=cf,d^b=dg81 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#92301, #72214448, #72214468, … |
| maximal normal subgroup of | D3×#92301, #72214448, #72214468, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1465);