Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of #10624600⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | #10624600⋊C2 |
| Fitting, Sylow | #10624600 ⋊ C2 |
| derived | #6861 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | #6861 | C2×C3 |
| Frattini | C33 | C3×C3⋊D3 |
| Fitting | #10624600 | C2 |
| socle | C32 | C3×#272 |
| LCS | G ▷ #6861 | |
| UCS | C1 | |
170 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 25 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 81 |
Polycyclic presentation:
2,3^6|b^3=fg,c^3=f^2,b^a=b^2f^2g^2,c^a=c^2f,e^a=ef^2g^2,f^a=f^2,g^a=g^2,c^b=ce,d^b=df,e^b=ef,e^c=eg50 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 827);