Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C23×C32 |
| direct product | C2×C32⋊#997 |
| unambiguous semidirect product | (C2×C32)⋊#997 |
| Fitting | C2×C32×H(5,𝔽2) ⋊ C3 |
| Sylow | C2×H(5,𝔽2) ⋊ H(3,𝔽3) |
1132 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 1132 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
134 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72220368, C2×(C3⋊#5935)⋊C3, C2×(C3⋊D3)⋊#997, … |
| maximal normal subgroup of | C2×#72220368, C2×(C3⋊#5935)⋊C3, C2×(C3⋊D3)⋊#997, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30950);