Finite Group DatabasebetaFinite Group Databasebeta| order | 11891 |
| isoclinism | isoclinic class of C23⋊C11 |
| automorphism | ? |
| homology | Abelianization (H1) = C11×C47 · Schur multiplier (H2) = C1 |
| direct product | C47×C23⋊C11 |
| unambiguous semidirect product | C23⋊(C11×C47) |
| unambiguous semidirect product | (C23×C47)⋊C11 |
| Fitting, socle, Hall | C23×C47 ⋊ C11 |
| derived, Sylow | C23 ⋊ C11×C47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C47 | C23⋊C11 |
| commutator, cosocle, hypocenter | C23 | C11×C47 |
| Frattini | C1 | G |
| Fitting, socle | C23×C47 | C11 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C47 | |
8 conjugacy classes of subgroups.
611 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C47×C23⋊C11, D47×C23⋊C11, C47×AGL(1,𝔽23), … |
| maximal normal subgroup of | C2×C47×C23⋊C11, D47×C23⋊C11, C47×AGL(1,𝔽23), … |
| maximal quotient of | C2×C47×C23⋊C11, C3×C47×C23⋊C11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11891, 2);