Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of C3⋊(C3⋊(C3⋊D3)) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C36 |
| direct product | C2×C3⋊(C3⋊(C3⋊(C3⋊C8))) |
| unambiguous semidirect product | (C2×C3)⋊(C3⋊(C3⋊(C3⋊C8))) |
| derived, Sylow | C34 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | C3⋊(C3⋊(C3⋊D3)) |
| commutator, hypocenter | C34 | C2×C8 |
| Frattini | C4 | C2×C3⋊(C3⋊(C3⋊D3)) |
| Fitting | C2×C34×C4 | C2 |
| socle, prime radical | C22×C34 | C4 |
| cosocle | C34×C4 | C22 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C2×C4 | |
2332 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1296 |
336 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2870);