Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #92265⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #92265⋊C4 |
| derived | C92 ⋊ C2×C3×C4 |
| Sylow | #6900 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #92265⋊C2 |
| commutator, hypocenter | C92 | C2×C3×C4 |
| Frattini, socle | C2×C32 | C3×D32 |
| Fitting | C2×#6900 | C22 |
| prime radical | C2×C3×AGL(1,ℤ/9) | D3 |
| cosocle | C2×C92 | C22×C3 |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C2 | |
216 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^2,3,2,3^4|b^2=d,e^3=h,f^3=g,f^a=f^2g^2,g^a=g^2,e^b=e^2h^2,h^b=h^2,e^c=eh^2,f^c=fg^272 conjugacy classes — view the full character table.
| maximal subgroup of | #72219877, C4×#92265⋊C2, #72219902, … |
| maximal normal subgroup of | #72219877, C4×#92265⋊C2, #72219902, … |
| maximal quotient of | #72219969, #72222406 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1220);