Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D32×C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C3 |
| direct product | C3×D32×C3⋊D3 |
| Fitting, socle, Sylow | C35 ⋊ C23 |
| derived | C34 ⋊ C23×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D32×C3⋊D3 |
| commutator, cosocle, hypocenter | C34 | C23×C3 |
| Frattini | C1 | G |
| Fitting, socle | C35 | C23 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C3 | |
2028 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 2028 conjugacy classes of subgroups — too many to draw. Only its 156 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D34, D33×C3⋊D3, D32×#1113, … |
| maximal normal subgroup of | C3×D34, D33×C3⋊D3, D32×#1113, … |
| maximal quotient of | D32×C3⋊AGL(1,ℤ/9), D32×C3⋊((C3⋊D3)⋊C3), C3×D3×((C3⋊D3)⋊C3)⋊D3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3933);