Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #272 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C22×C3×#1084 |
| derived | H(3,𝔽3) ⋊ C22×C3×C4 |
| Sylow | C3×H(3,𝔽3) ⋊ C22×C4 |
1056 conjugacy classes of subgroups; only the 278 normal subgroups are shown.
This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 278 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2660);