Finite Group Databasebeta

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C5⋊(C11⋊(D43⋊C3)) #28382016

order14190
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC5⋊(C11⋊(D43⋊C3))
unambiguous semidirect productC11⋊(C5⋊(D43⋊C3))
unambiguous semidirect product(C43⋊C3)⋊D55
unambiguous semidirect productD2365⋊C3

Splittings

Fitting, socle, derived, HallC5×C11×C43 ⋊ C2×C3
HallC5×C11×C43⋊C3 ⋊ C2
HallD2365 ⋊ C3
HallC11×C43⋊C3 ⋊ D5
HallC5×C43⋊C3 ⋊ D11
HallC11×C43 ⋊ C3×D5
HallC5×C43 ⋊ C3×D11
HallC43⋊C3 ⋊ D55
HallC5×C11 ⋊ D43⋊C3
SylowC43 ⋊ C3×D55
SylowC11 ⋊ C5⋊(D43⋊C3)
SylowC5 ⋊ C11⋊(D43⋊C3)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C11×C43C2×C3
LCSG ▷ C5×C11×C43
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2365

Polycyclic presentation:

2,3,5,11,43|c^a=c^4,d^a=d^10,e^a=e^42,e^b=e^36

Conjugacy classes & character table

472 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD55×D43⋊C3, D11×C5⋊(D43⋊C3), D5×C11⋊(D43⋊C3), …
maximal normal subgroup ofD55×D43⋊C3, D11×C5⋊(D43⋊C3), D5×C11⋊(D43⋊C3), …
maximal quotient ofC11⋊((C43⋊C3)⋊Dic5), C2×C5⋊(C11⋊(D43⋊C3))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14190, 33);