Finite Group DatabasebetaFinite Group Databasebeta| order | 3828 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D11×D87 |
| unambiguous semidirect product | (C3×D11)⋊D29 |
| unambiguous semidirect product | (D11×C29)⋊D3 |
| Fitting, socle, derived, Hall | C3×C11×C29 ⋊ C22 |
| Hall | C11×C29 ⋊ C2×D3 |
| Hall | C3×C29 ⋊ C2×D11 |
| Hall | C3×C11 ⋊ C2×D29 |
| Sylow | C29 ⋊ D3×D11 |
| Sylow | C11 ⋊ C2×D87 |
| Sylow | C3 ⋊ D11×D29 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C11×C29 | C22 |
| LCS | G ▷ C3×C11×C29 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 957 |
315 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D11×D261, C3×D11×D87, D11×C3⋊D87, … |
| maximal normal subgroup of | C3×D11×D87, AGL(1,𝔽11)×D87, C5×D11×D87, … |
| maximal quotient of | D11×D261, C3×D11×D87, D11×C3⋊D87, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3828, 18);