Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived | C22×H(3,𝔽3) ⋊ C3×C4 |
181 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 181 conjugacy classes of subgroups — too many to draw. Only its 23 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2,3,2^3,3^3|a^2=c,f^a=f^2,g^a=g^2h,d^b=de,e^b=d,f^b=fg,g^f=gh64 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 777);