Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C23×C3 |
| direct product | #97×(C3⋊D3)⋊C3 |
| unambiguous semidirect product | (C3⋊D3×#97)⋊C3 |
| Fitting | H(3,𝔽3)×#97 ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ C2×#97 |
551 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 551 conjugacy classes of subgroups — too many to draw. Only its 184 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | #97×PSU(3,𝔽2)⋊C3, #97×((C3⋊D3)⋊C3)⋊C2 |
| maximal normal subgroup of | #97×((C3⋊D3)⋊C3)⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 7591);