Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#88691 |
181 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 181 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2,3^3,2^2,3,2|a^2=h,b^3=d,e^2=h,f^2=h,g^a=g^2,c^b=cd,e^b=ef,f^b=e,f^e=fh93 conjugacy classes — view the full character table.
| maximal subgroup of | #72253016, #72253019, #72253021 |
| maximal normal subgroup of | #72253016 |
| maximal quotient of | #72253019 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2163);