Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #4183 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C22×C3×#4183 |
| Fitting | C22×C3×AΣL(1,𝔽27) ⋊ C2 |
| derived | AΣL(1,𝔽27) ⋊ C23×C3 |
| Sylow | C3×AΣL(1,𝔽27) ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | #4183 |
| commutator, cosocle, hypocenter | AΣL(1,𝔽27) | C23×C3 |
| Frattini | C32 | C22×C3×C3⋊D3 |
| Fitting | C22×C3×AΣL(1,𝔽27) | C2 |
| socle | C22×C32 | #272 |
| LCS | G ▷ AΣL(1,𝔽27) | |
| UCS | C1 ◁ C22×C3 | |
1098 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 1098 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#13091120, C3×A4×#4183, C3×D4×#4183, … |
| maximal normal subgroup of | C3×A4×#4183, C3×D4×#4183, C2×C3×C4×#4183, … |
| maximal quotient of | C3×D4×#4183, C2×C3×C4×#4183, C2×C3×C4⋊#4183, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2921);