Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2×C35 |
| unambiguous semidirect product | C3⋊(A4⋊#272) |
| unambiguous semidirect product | A4⋊(C3⋊#272) |
| Fitting | C22×C3×H(3,𝔽3) ⋊ D3 |
| derived | C3×A4×H(3,𝔽3) ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C3⋊(C3⋊(C3⋊S4)) |
| commutator, cosocle, hypocenter | C3×A4×H(3,𝔽3) | C2 |
| Fitting | C22×C3×H(3,𝔽3) | D3 |
| socle | C22×C32 | C3⋊(C3⋊D3) |
| LCS | G ▷ C3×A4×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
1511 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 1511 conjugacy classes of subgroups — too many to draw. Only its 249 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2,3^5,2^2|b^a=b^2,c^a=c^2,d^a=d^2,e^a=e^2,g^a=gh,g^b=h,h^b=gh,e^d=ef75 conjugacy classes — view the full character table.
| maximal subgroup of | #72259823 |
| maximal normal subgroup of | #72259823 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3622);