Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2×C32 |
| direct product | C3×A4⋊#272 |
| unambiguous semidirect product | A4⋊(C3×#272) |
| Fitting | C22×C3×H(3,𝔽3) ⋊ D3 |
| derived | A4×H(3,𝔽3) ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C3⋊(C3⋊S4) |
| commutator, cosocle, hypocenter | A4×H(3,𝔽3) | C2×C3 |
| Frattini | C3 | C3×C3⋊(C3⋊S4) |
| Fitting | C22×C3×H(3,𝔽3) | D3 |
| socle | C22×C32 | C3⋊(C3⋊D3) |
| LCS | G ▷ A4×H(3,𝔽3) | |
| UCS | C1 ◁ C32 | |
942 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 942 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
93 conjugacy classes — view the full character table.
| maximal quotient of | C3×A4⋊#4183, #72259823, #72259864, … |
| automorphism group of | #66364, #66365, #66366, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3611);