Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #6308 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C33 |
| direct product | C2×C3×#6312 |
| Fitting | C23×C34 ⋊ C2 |
| Sylow | C34 ⋊ C2×D4 |
2760 conjugacy classes of subgroups; only the 470 normal subgroups are shown.
This group has 2760 conjugacy classes of subgroups — too many to draw. Only its 470 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
342 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×C3⋊D3×#67, C2×#13049685, C2×#13049721, … |
| maximal normal subgroup of | C2×C3×C3⋊D3×#67, C2×#13049685, C2×#13049721, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3472);