Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of A4⋊((C3⋊D3)⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2×C33 |
| direct product | C3×A4⋊((C3⋊D3)⋊C3) |
| unambiguous semidirect product | A4⋊(C3×(C3⋊D3)⋊C3) |
| Fitting | C22×C3×H(3,𝔽3) ⋊ D3 |
| derived | C32×A4 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | A4⋊((C3⋊D3)⋊C3) |
| commutator, cosocle, hypocenter | C32×A4 | C2×C32 |
| Frattini | C3 | C32×C3⋊S4 |
| Fitting | C22×C3×H(3,𝔽3) | D3 |
| socle | C22×C32 | C3×C3⋊D3 |
| LCS | G ▷ C32×A4 | |
| UCS | C1 ◁ C3 | |
744 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 744 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
93 conjugacy classes — view the full character table.
| maximal subgroup of | C3×A4⋊#4183, #72259773, #72259823, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3595);