Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×D324 |
| Fitting | C2×C4×C81 ⋊ C2 |
| Sylow | C81 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D81 |
| commutator, cosocle | C2×C81 | C23 |
| Frattini | C2×C27 | C22×D3 |
| Fitting | C2×C4×C81 | C2 |
| socle | C22×C3 | C2×D27 |
| hypercenter | C2×C4 | D81 |
| hypocenter | C81 | C2×D4 |
| LCS | G ▷ C2×C81 ▷ C81 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
135 conjugacy classes of subgroups.
| transitive degree | μt(G) = 648 |
330 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 65);