Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C23×C32 |
No aliases for this group.
| Fitting | C32×#585 ⋊ C3 |
| Sylow | #585 ⋊ H(3,𝔽3) |
972 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 972 conjugacy classes of subgroups — too many to draw. Only its 53 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:
2,3^3,2^5|a^2=i,c^b=cd,e^b=ef,f^b=e,g^b=gh,h^b=g,h^e=hi,g^f=gi134 conjugacy classes — view the full character table.
| maximal subgroup of | #72242713, #72252743 |
| maximal normal subgroup of | #72242713, #72252743 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30953);