Finite Group DatabasebetaFinite Group Databasebeta| order | 10340 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C47⋊(Dic11⋊C5) |
| unambiguous semidirect product | (C11⋊C5)⋊Dic47 |
| unambiguous semidirect product | Dic517⋊C5 |
| derived, Hall | C11×C47 ⋊ C4×C5 |
| Hall | C47×C11⋊C5 ⋊ C4 |
| Hall | Dic517 ⋊ C5 |
| Hall | C11⋊C5 ⋊ Dic47 |
| Sylow | C47 ⋊ Dic11⋊C5 |
| Sylow | C11 ⋊ C5×Dic47 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C47⋊AGL(1,𝔽11) |
| commutator, hypocenter | C11×C47 | C4×C5 |
| Fitting, socle, cosocle | C2×C11×C47 | C2×C5 |
| prime radical | C2×C47×C11⋊C5 | C2 |
| LCS | G ▷ C11×C47 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,11,47,2|a^2=e,c^a=c^10,d^a=d^46,c^b=c^4344 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C47⋊(Dic11⋊C5), C3⋊(C47⋊(Dic11⋊C5)) |
| maximal normal subgroup of | C3×C47⋊(Dic11⋊C5) |
| maximal quotient of | C3×C47⋊(Dic11⋊C5), C3⋊(C47⋊(Dic11⋊C5)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10340, 12);