Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of A4⋊(D27⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | A4⋊(D27⋊C3) |
| Fitting | C22×C27⋊C3 ⋊ D3 |
| derived | A4×C27 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | A4×C27 | C2×C3 |
| Frattini | C9 | C3×C3⋊S4 |
| Fitting | C22×C27⋊C3 | D3 |
| socle | C22×C3 | C3×C3⋊D9 |
| LCS | G ▷ A4×C27 | |
| UCS | C1 | |
170 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 33 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:
2,3^5,2^2|d^3=e,e^3=f,c^a=c^2,d^a=d^2e^2f^2,e^a=e^2f^2,f^a=f^2,g^a=gh,d^b=df,g^c=h,h^c=gh75 conjugacy classes — view the full character table.
| maximal subgroup of | #72228977, S4×D27⋊C3, #72229343, … |
| maximal normal subgroup of | #72228977, S4×D27⋊C3, C2×A4⋊(D27⋊C3) |
| maximal quotient of | #72229343, C2×A4⋊(D27⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2418);