Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C33 · Schur multiplier (H2) = C2×C34 |
| direct product | C3×#67×H(3,𝔽3) |
| unambiguous semidirect product | (C32×#67)⋊C32 |
| Fitting | C22×C32×H(3,𝔽3) ⋊ C2 |
| Sylow | C32×H(3,𝔽3) ⋊ D4 |
1741 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 1741 conjugacy classes of subgroups — too many to draw. Only its 288 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
297 conjugacy classes. The character table is too large to display.
| maximal subgroup of | H(3,𝔽3)×#638⋊C3, C3×#67×(C3⋊D3)⋊C3, C3×#89039⋊C3, … |
| maximal normal subgroup of | C3×#67×(C3⋊D3)⋊C3, C3×#89039⋊C3, #67×C3⋊#272, … |
| maximal quotient of | H(3,𝔽3)×#638⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3294);