Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | #10624908⋊C2 |
| Fitting, Sylow | #10624908 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #4207⋊C3 |
| commutator, cosocle, hypocenter | C32⋊C9 | C2×C32 |
| Frattini, socle | C32 | C32×C3⋊D3 |
| Fitting | #10624908 | C2 |
| prime radical | #92304 | C3 |
| LCS | G ▷ C32⋊C9 | |
| UCS | C1 ◁ C3 | |
240 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
Polycyclic presentation:
2,3^6|b^3=g,c^3=g,d^3=f,e^3=f,b^a=bc^2d^2fg^2,c^a=d^2f,d^a=c^2,e^a=b^2de^2f,f^a=g^2,g^a=f^2,c^b=cf,d^b=dg,e^c=ef77 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1610);