Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of C3⋊(C3⋊D9) |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C33 |
| direct product | C23×C3⋊(C3⋊D9) |
| Fitting | C23×C32×C9 ⋊ C2 |
| derived, Sylow | C32×C9 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C3⋊(C3⋊D9) |
| commutator, cosocle, hypocenter | C32×C9 | C24 |
| Frattini | C3 | C23×C3⋊(C3⋊D3) |
| Fitting | C23×C32×C9 | C2 |
| socle | C23×C33 | D3 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 ◁ C23 | |
3350 conjugacy classes of subgroups.
| transitive degree | μt(G) = 648 |
336 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D4×C3⋊(C3⋊D9), C23×D9×C3⋊D3, C2×#13048710 |
| maximal normal subgroup of | C2×D4×C3⋊(C3⋊D9), C23×D9×C3⋊D3, C2×#13048710 |
| maximal quotient of | C2×D4×C3⋊(C3⋊D9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3075);