Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C3 |
No aliases for this group.
| Sylow | C33 ⋊ C2×#97 |
1180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^3|a^2=e,b^2=e,c^2=d,d^2=f,c^a=cf,g^a=g^2,h^a=h^2,c^b=cf,i^b=i^2204 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C3⋊D3×#97, #72245230, #72245396, … |
| maximal normal subgroup of | D3×C3⋊D3×#97, #72245230, #72245396, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 25593);