Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4×C8×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ #405 |
715 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 715 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^3|b^2=e,c^2=d,e^2=f,c^a=cf,g^a=g^2,h^a=h^2,h^g=hi248 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 9837);