Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #204 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C33 · Schur multiplier (H2) = C2×C33 |
| direct product | C33×D24 |
| Fitting | C34×C8 ⋊ C2 |
| Sylow | C34 ⋊ D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C33 | D12 |
| commutator, cosocle | C3×C4 | C22×C33 |
| Frattini | C4 | C2×C33×D3 |
| Fitting | C34×C8 | C2 |
| socle | C2×C34 | D4 |
| hypercenter | C33×C8 | D3 |
| hypocenter | C3 | C33×D8 |
| LCS | G ▷ C3×C4 ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C2×C33 ◁ C33×C4 ◁ C33×C8 | |
928 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
405 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2820);