Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D32×C3⋊D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C3 |
| direct product | D32×C3⋊D9 |
| Fitting, derived, Sylow | C33×C9 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C33×C9 | C23 |
| Frattini | C3 | D32×C3⋊D3 |
| socle | C34 | C22×D3 |
| LCS | G ▷ C33×C9 | |
| UCS | C1 | |
1098 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 1098 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
135 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#92280⋊C2, D32×C3⋊AGL(1,ℤ/9), D32×C9⋊D9, … |
| maximal normal subgroup of | D32×C3⋊AGL(1,ℤ/9), D33×D9 |
| maximal quotient of | D32×C9⋊D9, D3×D9×C3⋊D9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3568);