Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C33 · Schur multiplier (H2) = C23×C33 |
| direct product | C2×C33×#67 |
| Fitting | C23×C34 ⋊ C2 |
| Sylow | C34 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C33 | C2×D3 |
| commutator, cosocle | C2×C3 | C23×C33 |
| Frattini | C2 | C22×C33×D3 |
| Fitting | C23×C34 | C2 |
| socle | C22×C34 | C22 |
| hypercenter | C23×C33 | D3 |
| hypocenter | C3 | C2×C33×D4 |
| LCS | G ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C22×C33 ◁ C23×C33 | |
2760 conjugacy classes of subgroups; only the 756 normal subgroups are shown.
This group has 2760 conjugacy classes of subgroups — too many to draw. Only its 756 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
486 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C32×#3811, C2×C3×C3⋊D3×#67, C2×#13049685, … |
| maximal normal subgroup of | C2×C32×#3811, C2×C3×C3⋊D3×#67, C2×#13049685, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3452);