Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×SL(2,𝔽3)⋊(C22⋊C9) |
| unambiguous semidirect product | (C2×SL(2,𝔽3))⋊(C22⋊C9) |
| unambiguous semidirect product | (C2×#994)⋊C9 |
| derived | H(5,𝔽2) ⋊ C2×C3×C9 |
| Sylow | C2×H(5,𝔽2) ⋊ C3×C9 |
292 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72245009, C2×#13164076 |
| maximal normal subgroup of | C2×#72245009, C2×#13164076 |
| maximal quotient of | C2×#72244951, C2×#72244993 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30346);