Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #10619904⋊C3 |
| Sylow | H(5,𝔽3) ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #66432⋊C3 |
| commutator, cosocle | C2×C3×H(3,𝔽3) | C22×C3 |
| Frattini, socle | C2×C3 | C3×#1113 |
| Fitting | C2×H(5,𝔽3) | C22 |
| hypocenter | C3×H(3,𝔽3) | C3×D4 |
| LCS | G ▷ C2×C3×H(3,𝔽3) ▷ C3×H(3,𝔽3) | |
| UCS | C1 ◁ C2 | |
484 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 48 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:
2^2,3,2,3^4|b^a=bd,e^a=e^2,g^a=g^2,h^a=h^2,e^b=e^2,f^b=f^2,g^c=gh,f^e=fh85 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3147);