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C11⋊C5×D141 #29509331

order15510
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC11⋊C5×D141
unambiguous semidirect productC3⋊(C11⋊C5×D47)
unambiguous semidirect productC47⋊(D3×C11⋊C5)
unambiguous semidirect product(C11×D141)⋊C5

Splittings

Fitting, socle, derived, HallC3×C11×C47 ⋊ C2×C5
HallC3×C47×C11⋊C5 ⋊ C2
HallC11×D141 ⋊ C5
HallC47×C11⋊C5 ⋊ D3
HallC11×C47 ⋊ C5×D3
HallC3×C11⋊C5 ⋊ D47
HallC3×C47 ⋊ C2×C11⋊C5
SylowC47 ⋊ D3×C11⋊C5
HallC3×C11 ⋊ C5×D47
SylowC11 ⋊ C5×D141
SylowC3 ⋊ C11⋊C5×D47

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C47C2×C5
LCSG ▷ C3×C11×C47
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1551

Conjugacy classes & character table

504 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofAGL(1,𝔽11)×D141, D141⋊AGL(1,𝔽11), D3×C11⋊C5×D47, …
maximal normal subgroup ofAGL(1,𝔽11)×D141, D141⋊AGL(1,𝔽11), D3×C11⋊C5×D47, …
maximal quotient ofC11⋊C5×Dic141, C2×C11⋊C5×D141

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15510, 22);