Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C32 |
| unambiguous semidirect product | C4⋊(#4169⋊C3) |
| unambiguous semidirect product | (C4⋊#4169)⋊C3 |
| Fitting | C4×#6891 ⋊ C2 |
| Sylow | #6891 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×#4169⋊C3 |
| commutator, cosocle | C2×C3×C9 | C22×C32 |
| Frattini, socle | C2×C32 | C2×C32×D3 |
| Fitting | C4×#6891 | C2 |
| hypercenter | C4 | #4169⋊C3 |
| hypocenter | C3×C9 | C32×D4 |
| LCS | G ▷ C2×C3×C9 ▷ C3×C9 | |
| UCS | C1 ◁ C2 ◁ C4 | |
475 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 475 conjugacy classes of subgroups — too many to draw. Only its 81 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|b^2=e,f^3=h,b^a=be,f^a=f^2h^2,g^a=g^2,h^a=h^2,f^c=fh^2,f^d=fg129 conjugacy classes — view the full character table.
| maximal subgroup of | #72229211, D4×#4169⋊C3, #72259306, … |
| maximal normal subgroup of | #72229211, D4×#4169⋊C3, #72259306, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1712);