Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting, Sylow | #10624900 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊(C3⋊AGL(1,ℤ/9)) |
| commutator, cosocle, hypocenter | C9×H(3,𝔽3) | C2×C3 |
| Frattini, socle | C32 | C3×C3⋊(C3⋊D3) |
| Fitting | #10624900 | C2 |
| prime radical | C9⋊#272 | C3 |
| LCS | G ▷ C9×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
379 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
Polycyclic presentation:
2,3^6|b^3=g,d^3=f,b^a=b^2f^2g^2,c^a=c^2f,e^a=e^2f,g^a=g^2,c^b=cf,d^b=dg,e^c=ef74 conjugacy classes — view the full character table.
| maximal subgroup of | #72221823, #72221864, C2×#13091524 |
| maximal normal subgroup of | #72221823, #72221864, C2×#13091524 |
| maximal quotient of | #72221827, C2×#13091524 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1598);