Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C22×C32 |
| Fitting | C23×C33 ⋊ C2×C3 |
548 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #67×C22⋊H(3,𝔽3), C2×D3×(C3⋊D3)⋊A4, #72222927, … |
| maximal normal subgroup of | #67×C22⋊H(3,𝔽3), C2×D3×(C3⋊D3)⋊A4, #72222927, … |
| maximal quotient of | #67×C22⋊H(3,𝔽3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3017);