Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of C9⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C32 · Schur multiplier (H2) = C27 |
| direct product | C24×#1094 |
| Sylow | C26 ⋊ 3−1+2 |
6454 conjugacy classes of subgroups; only the 670 normal subgroups are shown.
This group has 6454 conjugacy classes of subgroups — too many to draw. Only its 670 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C24×C3×#1094, C22×#13049240, C22×A4×#1094, … |
| maximal normal subgroup of | C24×C3×#1094, C22×#13049240, C22×A4×#1094, … |
| maximal quotient of | C24×C3×#1094, #72245329, C22×D4×#1094 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 46169);