Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of C9⋊SL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C32 |
| direct product | C2×C3×#6204 |
| Sylow | C2×Q8 ⋊ C3×3−1+2 |
378 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
186 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14517252, C2×C3×#11722589, C2×C3×#88691, … |
| maximal normal subgroup of | C2×#14517252, C2×C3×#88691, C2×C3⋊(#3689⋊C3) |
| maximal quotient of | C2×#14517252 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2534);