Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C22×C32 |
| direct product | C2×S4×H(3,𝔽3) |
| unambiguous semidirect product | A4⋊(C22×H(3,𝔽3)) |
| unambiguous semidirect product | (C2×A4)⋊(C2×H(3,𝔽3)) |
| unambiguous semidirect product | (C2×C32×S4)⋊C3 |
| Fitting | C23×H(3,𝔽3) ⋊ D3 |
431 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 431 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
110 conjugacy classes — view the full character table.
| maximal subgroup of | C2×S4×(C3⋊D3)⋊C3, C2×S4×#272, C2×H(3,𝔽3)×GL(3,𝔽2) |
| maximal normal subgroup of | C2×S4×(C3⋊D3)⋊C3, C2×S4×#272 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2987);