Finite Group DatabasebetaFinite Group Databasebeta| order | 4356 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D11×D33 |
| unambiguous semidirect product | (C3×D11)⋊(C3×D11) |
| unambiguous semidirect product | (C11×D11)⋊(C3×D3) |
| Fitting, socle, Hall | C32×C112 ⋊ C22 |
| derived | C3×C112 ⋊ C22×C3 |
| Sylow | C112 ⋊ C2×C3×D3 |
| Sylow | C32 ⋊ D112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D11×D33 |
| commutator, cosocle, hypocenter | C3×C112 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C112 | C22 |
| LCS | G ▷ C3×C112 | |
| UCS | C1 ◁ C3 | |
133 conjugacy classes of subgroups.
| transitive degree | μt(G) = 132 |
378 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4356, 96);