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 | C8×C3⋊(C3⋊(C3⋊D3)) |
| Fitting | C34×C8 ⋊ C2 |
| derived, Sylow | C34 ⋊ C2×C8 |
2332 conjugacy classes of subgroups.
| transitive degree | μt(G) = 648 |
336 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2865);