Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, Sylow | #10624905 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #92391 |
| commutator, cosocle, hypocenter | C3×H(3,𝔽3) | C2×C32 |
| Frattini, socle | C32 | C32×C3⋊D3 |
| Fitting | #10624905 | C2 |
| prime radical | #92300 | C3 |
| LCS | G ▷ C3×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
302 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 302 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=fg,c^3=fg,b^a=cd^2e,c^a=bd^2e,d^a=e,e^a=d,f^a=g,g^a=f,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, 1606);