Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C3⋊(A4⋊((C3⋊D3)⋊C3)) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2×C34 |
| unambiguous semidirect product | C3⋊(A4⋊((C3⋊D3)⋊C3)) |
| unambiguous semidirect product | A4⋊(C3⋊((C3⋊D3)⋊C3)) |
| Fitting | C22×C3×H(3,𝔽3) ⋊ D3 |
| derived | C33×A4 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C33×A4 | C2×C3 |
| Frattini | C3 | C3×C3⋊(C3⋊S4) |
| Fitting | C22×C3×H(3,𝔽3) | D3 |
| socle | C22×C32 | C3×C3⋊D3 |
| LCS | G ▷ C33×A4 | |
| UCS | C1 | |
1005 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 1005 conjugacy classes of subgroups — too many to draw. Only its 96 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|c^a=c^2,d^a=d^2,e^a=e^2,f^a=f^2,g^a=gh,e^b=ef,g^c=h,h^c=gh75 conjugacy classes — view the full character table.
| maximal quotient of | #72259823 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3612);