Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C32 · Schur multiplier (H2) = C26×C3 |
| direct product | C23×C32×D9 |
| Fitting | C23×C32×C9 ⋊ C2 |
| derived | C9 ⋊ C24×C32 |
| Sylow | C32×C9 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C32 | D9 |
| commutator, cosocle, hypocenter | C9 | C24×C32 |
| Frattini | C3 | C23×C32×D3 |
| Fitting | C23×C32×C9 | C2 |
| socle | C23×C33 | D3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C23×C32 | |
1462 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
432 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C32×D4×D9, C23×D9×C3⋊D3, C2×D9×#638 |
| maximal normal subgroup of | C2×C32×D4×D9, C23×D9×C3⋊D3, C2×D9×#638 |
| maximal quotient of | C2×C32×D4×D9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3062);