Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of #4177⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting, Sylow | #10624690 ⋊ C2 |
| derived | C3×C9 ⋊ C2×C3×C9 |
179 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 179 conjugacy classes of subgroups — too many to draw. Only its 38 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=f,c^3=g,c^a=c^2g^2,e^a=e^2,g^a=g^2,c^b=ce,e^b=eg,d^c=dg93 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 983);