Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of (C3⋊S4)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24×C3 |
| direct product | C22×(C3⋊SL(2,ℤ/4))⋊C3 |
| derived | C3×A4 ⋊ C22×C3×C4 |
1232 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 150 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
152 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#64269⋊C3 |
| maximal normal subgroup of | C22×#64269⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30510);