Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C3⋊(C3⋊((C3⋊D3)⋊A4)) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2×C34 |
| unambiguous semidirect product | C3⋊(C3⋊((C3⋊D3)⋊A4)) |
| Fitting, derived | C22×C34 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C22×C34 | C2×C3 |
| Frattini | C3 | A4×C3⋊(C3⋊D3) |
| socle | C22×C33 | C3×D3 |
| LCS | G ▷ C22×C34 | |
| UCS | C1 | |
1760 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 1760 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
Polycyclic presentation:
2,3,2^2,3^4|e^a=e^2,f^a=f^2,g^a=g^2,h^a=h^2,c^b=d,d^b=cd,g^b=gh96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3668);