Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C23×C32 |
No aliases for this group.
| Fitting | C22×C32×#41 ⋊ C3 |
| Sylow | C22×#41 ⋊ H(3,𝔽3) |
1034 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 1034 conjugacy classes of subgroups — too many to draw. Only its 56 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:
2,3^3,2^5|a^2=i,g^2=i,h^2=i,c^b=cd,e^b=ef,f^b=e,g^b=gh,h^b=g,h^g=hi152 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30947);