Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | C3⋊#10619773 |
| Fitting, derived | C22×C3×H(3,𝔽3) ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊((C3⋊D3)⋊A4) |
| commutator, Fitting, cosocle, hypocenter | C22×C3×H(3,𝔽3) | C2×C3 |
| Frattini | C32 | A4×C3⋊D3 |
| socle | C22×C32 | (C3⋊D3)⋊C3 |
| LCS | G ▷ C22×C3×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
477 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 477 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) = 72 |
Polycyclic presentation:
2,3,2^2,3^4|e^a=e^2,f^a=f^2,g^a=g^2,c^b=d,d^b=cd,f^b=fgh,g^f=gh^260 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2654);