Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #4207⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2×C32 |
| unambiguous semidirect product | #4207⋊A4 |
| Fitting | C22×#737 ⋊ C2×C3 |
| derived | C22×C3×C9 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C22×C3×C9 | C2×C32 |
| Frattini | C3 | C3×A4×C3⋊D3 |
| Fitting | C22×#737 | C2×C3 |
| socle | C22×C3 | C32×C3⋊D3 |
| LCS | G ▷ C22×C3×C9 | |
| UCS | C1 | |
431 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 431 conjugacy classes of subgroups — too many to draw. Only its 58 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:
2,3^2,2^2,3^3|g^3=h,f^a=f^2,g^a=g^2h^2,h^a=h^2,d^b=de,e^b=d,g^b=gh^2,f^c=fh^276 conjugacy classes — view the full character table.
| maximal subgroup of | A4×#4207⋊C3 |
| maximal normal subgroup of | A4×#4207⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3655);