Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C32 |
| unambiguous semidirect product | #10619983⋊C3 |
| Fitting | C22×3−1+4 ⋊ C2 |
| Sylow | 3−1+4 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×#4207⋊C3 |
| commutator, cosocle | C2×C3×C9 | C22×C32 |
| Frattini, socle | C2×C3 | C2×C32×C3⋊D3 |
| Fitting | C22×3−1+4 | C2 |
| hypercenter | C22 | #4207⋊C3 |
| hypocenter | C3×C9 | C32×D4 |
| LCS | G ▷ C2×C3×C9 ▷ C3×C9 | |
| UCS | C1 ◁ C2 ◁ C22 | |
817 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 817 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2^2,3^2,2,3^3|g^3=h,b^a=be,f^a=f^2,g^a=g^2h^2,h^a=h^2,g^c=gh^2,f^d=fh^2193 conjugacy classes — view the full character table.
| maximal subgroup of | #72228545, D4×#4207⋊C3, #72229247, … |
| maximal normal subgroup of | D4×#4207⋊C3, #72229247, #72259345, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3364);