Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of C3⋊((C3⋊D3)⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2×C32 |
| direct product | C8×C3⋊((C3⋊D3)⋊C3) |
| Fitting | C3×C8×H(3,𝔽3) ⋊ C2 |
| derived | C33 ⋊ C2×C3×C8 |
| Sylow | C3×H(3,𝔽3) ⋊ C2×C8 |
346 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1614);