Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24×C3 |
No aliases for this group.
| Sylow | C33 ⋊ B(4,𝔽2) |
1708 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 1708 conjugacy classes of subgroups — too many to draw. Only its 164 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^6,3^3|a^2=e,b^a=be,c^a=cd,d^a=df,g^a=g^2,h^a=h^2,d^b=df,i^b=i^2,e^c=ef135 conjugacy classes — view the full character table.
| maximal subgroup of | #72220851, D3×#10591531, #72258275 |
| maximal normal subgroup of | #72220851, D3×#10591531, #72258275 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 27008);