Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of C3⋊(C3⋊D9) |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C33×C4 |
| direct product | C4×C3⋊(C3⋊Dic9) |
| derived, Sylow | C32×C9 ⋊ C42 |
750 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1296 |
336 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C3⋊D3×Dic9 |
| maximal normal subgroup of | C4×C3⋊D3×Dic9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1727);