Finite Group DatabasebetaFinite Group Databasebeta| order | 4708 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D11×D107 |
| unambiguous semidirect product | (D11×C107)⋊C2 |
| unambiguous semidirect product | (C11×D107)⋊C2 |
| unambiguous semidirect product | D1177⋊C2 |
| Fitting, socle, derived, Hall | C11×C107 ⋊ C22 |
| Sylow | C107 ⋊ C2×D11 |
| Sylow | C11 ⋊ C2×D107 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C107 | C22 |
| LCS | G ▷ C11×C107 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 118 |
| transitive degree | μt(G) = 1177 |
385 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D11×D107, D33×D107, D11×D321, … |
| maximal normal subgroup of | C3×D11×D107, AGL(1,𝔽11)×D107, C5×D11×D107, … |
| maximal quotient of | C3×D11×D107, D33×D107, D11×D321, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4708, 6);