Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2×C33 |
| direct product | H(3,𝔽3)×C3⋊S4 |
| unambiguous semidirect product | C3⋊(S4×H(3,𝔽3)) |
| unambiguous semidirect product | A4⋊(D3×H(3,𝔽3)) |
| Fitting | C22×C3×H(3,𝔽3) ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C32×C3⋊S4 |
| commutator, cosocle | C32×A4 | C2×C32 |
| Fitting | C22×C3×H(3,𝔽3) | D3 |
| socle | C22×C32 | C32×D3 |
| hypercenter | H(3,𝔽3) | C3⋊S4 |
| hypocenter | C3×A4 | C2×H(3,𝔽3) |
| LCS | G ▷ C32×A4 ▷ C3×A4 | |
| UCS | C1 ◁ C3 ◁ H(3,𝔽3) | |
731 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 731 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
99 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3593);