Finite Group DatabasebetaFinite Group Databasebeta| order | 11396 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D11×D259 |
| unambiguous semidirect product | (C7×D11)⋊D37 |
| unambiguous semidirect product | (D11×C37)⋊D7 |
| Fitting, socle, derived, Hall | C7×C11×C37 ⋊ C22 |
| Hall | C11×C37 ⋊ C2×D7 |
| Hall | C7×C37 ⋊ C2×D11 |
| Hall | C7×C11 ⋊ C2×D37 |
| Sylow | C37 ⋊ D7×D11 |
| Sylow | C11 ⋊ C2×D259 |
| Sylow | C7 ⋊ D11×D37 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C11×C37 | C22 |
| LCS | G ▷ C7×C11×C37 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
917 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#13095537, D11×#13095538, D11×ΓL(1,𝔽8)⋊D37, … |
| maximal normal subgroup of | D11×#13095537, D11×#13095538, D11×ΓL(1,𝔽8)⋊D37, … |
| maximal quotient of | C3×D11×D259, D11×D777, D33×D259, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11396, 18);