Finite Group DatabasebetaFinite Group Databasebeta| order | 11748 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C11⋊#67063) |
| unambiguous semidirect product | C11⋊(C3⋊#67063) |
| Fitting, socle, derived, Hall | C3×C11×C89 ⋊ C4 |
| Hall | C11×C89 ⋊ Dic3 |
| Hall | C3×C89 ⋊ Dic11 |
| Sylow | C89 ⋊ Dic33 |
| Hall | C3×C11 ⋊ #67063 |
| Sylow | C11 ⋊ C3⋊#67063 |
| Sylow | C3 ⋊ C11⋊#67063 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C11×C89 | C4 |
| prime radical, cosocle | C3×C11×D89 | C2 |
| LCS | G ▷ C3×C11×C89 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,11,89|a^2=b,c^a=c^2,d^a=d^10,e^a=e^55,e^b=e^88762 conjugacy classes — view the full character table.
| maximal subgroup of | C9⋊(C11⋊#67063), C3×C3⋊(C11⋊#67063), C3⋊(C3⋊(C11⋊#67063)) |
| maximal normal subgroup of | C3×C3⋊(C11⋊#67063) |
| maximal quotient of | C9⋊(C11⋊#67063), C3×C3⋊(C11⋊#67063), C3⋊(C3⋊(C11⋊#67063)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11748, 27);