Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C3×A4×#217 |
| unambiguous semidirect product | (C22×#217)⋊C32 |
| unambiguous semidirect product | (C22×C3×#217)⋊C3 |
1182 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 1182 conjugacy classes of subgroups — too many to draw. Only its 152 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | A4×#1094⋊C4, C3×A4×#953 |
| maximal normal subgroup of | C3×A4×#953 |
| maximal quotient of | #217×#1094 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 39199);