Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | H(3,𝔽3) ⋊ #551 |
1364 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1364 conjugacy classes of subgroups — too many to draw. Only its 219 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^6,3^3|a^2=f,c^2=e,d^a=de,g^a=g^2,h^a=h^2,c^b=cf,d^c=de,h^g=hi131 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 20080);