Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | Q8×D81 |
| Fitting | Q8×C81 ⋊ C2 |
| Sylow | C81 ⋊ C2×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×D81 |
| commutator, cosocle | C2×C81 | C23 |
| Frattini | C2×C27 | C22×D3 |
| Fitting | Q8×C81 | C2 |
| socle | C2×C3 | C22×D27 |
| prime radical | C2×D81 | C22 |
| hypercenter | Q8 | D81 |
| hypocenter | C81 | C2×Q8 |
| LCS | G ▷ C2×C81 ▷ C81 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
95 conjugacy classes of subgroups.
| transitive degree | μt(G) = 648 |
210 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 69);