Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×D3×#272 |
| Fitting | C3×C4×H(3,𝔽3) ⋊ C22 |
| derived, Sylow | C3×H(3,𝔽3) ⋊ C22×C4 |
730 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#11757730, D3×AGL(1,𝔽5)×#272, D3×D4×#272 |
| maximal normal subgroup of | D3×D4×#272 |
| maximal quotient of | C4×#11757730, D3×AGL(1,𝔽5)×#272 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2399);