Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D3×C3⋊D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C32 |
| direct product | D3×C3⋊D32 |
| Fitting, socle, derived, Sylow | C35 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C35 | C23 |
| LCS | G ▷ C35 | |
| UCS | C1 | |
3536 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 3536 conjugacy classes of subgroups — too many to draw. Only its 166 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#10620206, D3×#11757731, D3×#10620198, … |
| maximal normal subgroup of | D3×#10620206, D3×#10620198, D3×#11757702, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3937);