Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #10624795⋊C2 |
| Fitting, Sylow | #10624795 ⋊ C2 |
145 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 145 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 243 |
Polycyclic presentation:
2,3^6|c^3=eg,b^a=bd,d^a=d^2,f^a=f^2,c^b=ce,d^b=df,f^b=fg,f^d=fg86 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1307);