Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of C3⋊#226 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3×C3⋊GU(2,𝔽3) |
| unambiguous semidirect product | (C2×C3)⋊(C3×GU(2,𝔽3)) |
| derived | C3×SL(2,𝔽3) ⋊ C2×C3×C4 |
527 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 527 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×#10593663 |
| maximal normal subgroup of | C2×C3×#10593663 |
| maximal quotient of | C2×#72252951 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 39087);