Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #4184⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #4184⋊A4 |
| Fitting, derived | C22×#731 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C22×#731 | C2×C3 |
| Frattini | C32 | A4×C3⋊D3 |
| socle | C22×C3 | C3×#272 |
| LCS | G ▷ C22×#731 | |
| UCS | C1 | |
244 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 28 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:
2,3,2^2,3^4|f^3=h^2,e^a=e^2,f^a=f^2h,h^a=h^2,c^b=d,d^b=cd,f^b=fh,f^e=fg,g^e=gh,g^f=gh^244 conjugacy classes — view the full character table.
| maximal subgroup of | A4×#4184⋊C3 |
| maximal normal subgroup of | A4×#4184⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2633);