Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C2×C32 |
| direct product | H(3,𝔽3)×SL(2,ℤ/4) |
| unambiguous semidirect product | A4⋊(C4×H(3,𝔽3)) |
| unambiguous semidirect product | (C32×SL(2,ℤ/4))⋊C3 |
277 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 277 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
110 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2085);