Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of A4×#4183 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
| direct product | A4×#4183 |
| Fitting, derived | C22×AΣL(1,𝔽27) ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C22×AΣL(1,𝔽27) | C2×C3 |
| Frattini | C32 | A4×C3⋊D3 |
| socle | C22×C3 | C3×#272 |
| LCS | G ▷ C22×AΣL(1,𝔽27) | |
| UCS | C1 | |
380 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 29 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
52 conjugacy classes — view the full character table.
| maximal subgroup of | C3×A4×#4183, A4×#4183⋊C3 |
| maximal normal subgroup of | C3×A4×#4183, A4×#4183⋊C3 |
| maximal quotient of | C3×A4×#4183 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2630);