Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, Sylow | #10624765 ⋊ C2 |
605 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 605 conjugacy classes of subgroups — too many to draw. Only its 27 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 18 |
Polycyclic presentation:
2,3^6|b^3=e,d^a=d^2,f^a=f^2,g^a=g^2,c^b=ce,d^b=df,f^b=fg69 conjugacy classes — view the full character table.
| maximal subgroup of | #72277583, #72277733 |
| maximal normal subgroup of | #72277733 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1242);