Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C32 |
| direct product | C22×C3×C3⋊#272 |
| Fitting | C22×C32×H(3,𝔽3) ⋊ C2 |
| derived | C3×H(3,𝔽3) ⋊ C23×C3 |
| Sylow | C32×H(3,𝔽3) ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C32 | C3⋊(C3⋊D3) |
| commutator, cosocle, hypocenter | C3×H(3,𝔽3) | C23×C3 |
| Frattini | C3 | C22×C3×C3⋊(C3⋊D3) |
| Fitting | C22×C32×H(3,𝔽3) | C2 |
| socle | C22×C33 | C3⋊D3 |
| LCS | G ▷ C3×H(3,𝔽3) | |
| UCS | C1 ◁ C22×C32 | |
2853 conjugacy classes of subgroups; only the 342 normal subgroups are shown.
This group has 2853 conjugacy classes of subgroups — too many to draw. Only its 342 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#13091502, C22×#11758090, C3×#13048733, … |
| maximal normal subgroup of | C22×#11758090, C3×#13048733, #67×C3⋊#272, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3769);