Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C4⋊(C3⋊AGL(1,ℤ/9)) |
| Fitting | C2×C3×C4×3−1+2 ⋊ C2 |
| Sylow | C3×3−1+2 ⋊ C2×D4 |
612 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 150 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C4⋊#92314, C2×D4×C3⋊AGL(1,ℤ/9), #72219922, … |
| maximal normal subgroup of | C2×D4×C3⋊AGL(1,ℤ/9), #72219922, #72219923, … |
| maximal quotient of | C2×C4⋊#92314, #72219940, #72220049, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2617);