Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C3⋊#4185 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C33 |
| direct product | C2×C3⋊#66332 |
| unambiguous semidirect product | (C2×C3)⋊#66332 |
| derived, Sylow | C3×#732 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C3⋊#4185 |
| commutator, hypocenter | C3×#732 | C2×C4 |
| Frattini | C2×C32 | C2×C3⋊(C3⋊D3) |
| Fitting, prime radical | C22×C3×#732 | C2 |
| socle | C22×C32 | #272 |
| cosocle | C2×C3×#732 | C22 |
| LCS | G ▷ C3×#732 | |
| UCS | C1 ◁ C22 | |
606 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 606 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 648 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2157);