Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C1 |
| direct product | 3−1+2×GL(2,𝔽3) |
| unambiguous semidirect product | (C9×GL(2,𝔽3))⋊C3 |
| Fitting | Q8×3−1+2 ⋊ D3 |
161 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 161 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | 3−1+2×#5935, GL(2,𝔽3)×AGL(1,ℤ/9), #72253010 |
| maximal normal subgroup of | GL(2,𝔽3)×AGL(1,ℤ/9) |
| maximal quotient of | #72253004 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2083);