Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24×C3 |
No aliases for this group.
| Fitting | C24×C33 ⋊ C22 |
| Sylow | C33 ⋊ B(4,𝔽2) |
1708 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 1708 conjugacy classes of subgroups — too many to draw. Only its 134 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|c^a=ce,d^a=df,g^a=g^2,h^a=h^2,c^b=cd,e^b=ef,i^b=i^2150 conjugacy classes — view the full character table.
| maximal subgroup of | #72220693, #72220728, #72220851, … |
| maximal normal subgroup of | #72220851, D3×#10591725, #72220954 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 27525);