Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of SL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C9 · Schur multiplier (H2) = C33 |
| direct product | C2×C32×Q8⋊C9 |
| derived | Q8 ⋊ C2×C32×C9 |
| Sylow | C2×Q8 ⋊ C32×C9 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical, hypercenter | C22×C33 | A4 |
| commutator, hypocenter | Q8 | C2×C32×C9 |
| Frattini | C2×C3 | C2×C32×A4 |
| Fitting | C2×C33×Q8 | C3 |
| cosocle | C3×Q8 | C2×C33 |
| LCS | G ▷ Q8 | |
| UCS | C1 ◁ C22×C33 | |
462 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1296 |
378 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2533);