Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of C9⋊(C22⋊A4) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C25×C32 |
| direct product | C22×C32⋊(C22⋊A4) |
| Fitting | C26×C32 ⋊ C3 |
| Sylow | C26 ⋊ H(3,𝔽3) |
5965 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 5965 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | C22×(C22⋊A4)⋊H(3,𝔽3), C22×#11724052, C22×(C3⋊D3)⋊(C22⋊A4), … |
| maximal normal subgroup of | C22×(C22⋊A4)⋊H(3,𝔽3), C22×#11724052, C22×(C3⋊D3)⋊(C22⋊A4), … |
| maximal quotient of | #72252743 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 46175);