Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of #6249⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×#6249⋊C2 |
| unambiguous semidirect product | #6249⋊C23 |
| unambiguous semidirect product | SU(3,𝔽2)⋊C23 |
| Fitting | C22×H(3,𝔽3) ⋊ SD16 |
| Sylow | H(3,𝔽3) ⋊ C22×SD16 |
581 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 581 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
56 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13164090, C23×#6249⋊C2 |
| maximal normal subgroup of | C2×#13164090, C23×#6249⋊C2 |
| maximal quotient of | C2×#13164090, C23×#6249⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 46113);