Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C33 |
| direct product | C2×C4⋊(C3⋊(C3⋊D9)) |
| Fitting | C2×C32×C4×C9 ⋊ C2 |
| Sylow | C32×C9 ⋊ C2×D4 |
1350 conjugacy classes of subgroups; only the 411 normal subgroups are shown.
This group has 1350 conjugacy classes of subgroups — too many to draw. Only its 411 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 648 |
330 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3⋊D3×D36, C2×D4×C3⋊(C3⋊D9), C2×D9×C4⋊(C3⋊D3) |
| maximal normal subgroup of | C2×C3⋊D3×D36, C2×D4×C3⋊(C3⋊D9), C2×D9×C4⋊(C3⋊D3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2671);