Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C3⋊#4175 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C32 |
| direct product | C22×C3⋊#4175 |
| Fitting | C22×C3×AΣL(1,𝔽27) ⋊ C2 |
| derived | C34 ⋊ C23×C3 |
| Sylow | C3×AΣL(1,𝔽27) ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C3⋊#4175 |
| commutator, cosocle, hypocenter | C34 | C23×C3 |
| Frattini | C32 | C22×C3×C3⋊D3 |
| Fitting | C22×C3×AΣL(1,𝔽27) | C2 |
| socle | C22×C32 | (C3⋊D3)⋊C3 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C22 | |
1584 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 1584 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2923);