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C11⋊C5×D43⋊C3 #28382017

order14190
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC11⋊C5×D43⋊C3
unambiguous semidirect productD43⋊(C3×C11⋊C5)
unambiguous semidirect product(C43⋊C3)⋊(C2×C11⋊C5)
unambiguous semidirect product(C11×D43⋊C3)⋊C5
unambiguous semidirect product(C11⋊C5×D43)⋊C3

Splittings

Fitting, socle, derived, HallC11×C43 ⋊ C2×C3×C5
HallC11⋊C5×C43⋊C3 ⋊ C2
HallC11⋊C5×D43 ⋊ C3
HallC11×D43⋊C3 ⋊ C5
HallC43×C11⋊C5 ⋊ C2×C3
HallC11×C43⋊C3 ⋊ C2×C5
HallC11×D43 ⋊ C3×C5
HallC43⋊C3 ⋊ C2×C11⋊C5
HallD43 ⋊ C3×C11⋊C5
SylowC43 ⋊ C2×C3×C11⋊C5
SylowC11 ⋊ C5×D43⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC11×C43C2×C3×C5
LCSG ▷ C11×C43
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 473

Conjugacy classes & character table

91 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽11)×D43⋊C3, C2×C11⋊C5×D43⋊C3
maximal normal subgroup ofAGL(1,𝔽11)×D43⋊C3, C2×C11⋊C5×D43⋊C3
maximal quotient ofC11⋊C5×(C43⋊C3)⋊C4, C2×C11⋊C5×D43⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14190, 34);