Finite Group DatabasebetaFinite Group Databasebeta| order | 3924 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D3×D109 |
| Fitting, socle, Hall | C32×C109 ⋊ C22 |
| derived | C3×C109 ⋊ C22×C3 |
| Sylow | C109 ⋊ C2×C3×D3 |
| Sylow | C32 ⋊ C2×D109 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3×D109 |
| commutator, cosocle, hypocenter | C3×C109 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C109 | C22 |
| LCS | G ▷ C3×C109 | |
| UCS | C1 ◁ C3 | |
44 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 654 |
504 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×D3×D109, C3×D15×D109, C3×D3×D545, … |
| maximal normal subgroup of | C3×C5×D3×D109, C3×D3×C7×D109 |
| maximal quotient of | C3×C5×D3×D109, C3×D15×D109, C3×D3×D545, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3924, 45);