Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of (C3⋊#226)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C4×(C3⋊GL(2,𝔽3))⋊C3 |
| unambiguous semidirect product | (C4×C3⋊GL(2,𝔽3))⋊C3 |
| Fitting | C32×C4×Q8 ⋊ D3 |
| derived | C3×SL(2,𝔽3) ⋊ C2×C3×C4 |
347 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 347 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) = 288 |
116 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 12888);