Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of (A4⋊((C3⋊D3)⋊C3))⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2×C32 |
| unambiguous semidirect product | (A4⋊((C3⋊D3)⋊C3))⋊C3 |
| Fitting | C22×C3×H(3,𝔽3) ⋊ D3 |
| derived | C32×A4 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C32×A4 | C2×C32 |
| Frattini | C3 | C32×C3⋊S4 |
| Fitting | C22×C3×H(3,𝔽3) | D3 |
| socle | C22×C3 | C32×C3⋊D3 |
| LCS | G ▷ C32×A4 | |
| UCS | C1 | |
524 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
Polycyclic presentation:
2,3^5,2^2|d^a=d^2,e^a=e^2,f^a=f^2,g^a=gh,e^b=ef,d^c=df^2,g^d=h,h^d=gh85 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3596);