Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #4183⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C22×#4183⋊C3 |
| Fitting | C22×#6909 ⋊ C2 |
| derived | AΣL(1,𝔽27) ⋊ C23×C3 |
| Sylow | #6909 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #4183⋊C3 |
| commutator, cosocle, hypocenter | AΣL(1,𝔽27) | C23×C3 |
| Frattini | C32 | C22×C3×C3⋊D3 |
| Fitting | C22×#6909 | C2 |
| socle | C22×C3 | C3×#272 |
| LCS | G ▷ AΣL(1,𝔽27) | |
| UCS | C1 ◁ C22 | |
752 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#13091120, A4×#4183⋊C3, D4×#4183⋊C3 |
| maximal normal subgroup of | A4×#4183⋊C3, D4×#4183⋊C3 |
| maximal quotient of | D4×#4183⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2932);