Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C9 |
| unambiguous semidirect product | C4⋊#92309 |
| Fitting | C4×#6896 ⋊ C2 |
| Sylow | #6896 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×#92309 |
| commutator, cosocle | C2×C92 | C22×C3 |
| Frattini, socle | C2×C32 | C2×C3×C3⋊D3 |
| Fitting | C4×#6896 | C2 |
| hypercenter | C4 | #92309 |
| hypocenter | C92 | C3×D4 |
| LCS | G ▷ C2×C92 ▷ C92 | |
| UCS | C1 ◁ C2 ◁ C4 | |
324 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 324 |
Polycyclic presentation:
2^2,3,2,3^4|b^2=d,e^3=h,f^3=g,b^a=bd,e^a=e^2h^2,f^a=f^2g^2,g^a=g^2,h^a=h^2,e^c=eh,f^c=fg^2111 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1943);