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C3×C53⋊AGL(1,𝔽11) #31775825

order17490
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C53⋊AGL(1,𝔽11)
unambiguous semidirect productC53⋊(C3×AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(C3×D53)
unambiguous semidirect productD583⋊(C3×C5)
unambiguous semidirect product(C3×D583)⋊C5

Splittings

Fitting, socle, HallC3×C11×C53 ⋊ C2×C5
derived, HallC11×C53 ⋊ C2×C3×C5
HallC3×C53×C11⋊C5 ⋊ C2
HallC3×D583 ⋊ C5
HallC53×C11⋊C5 ⋊ C2×C3
HallD583 ⋊ C3×C5
HallC3×C11⋊C5 ⋊ D53
HallC3×C53 ⋊ AGL(1,𝔽11)
HallC11⋊C5 ⋊ C3×D53
SylowC53 ⋊ C3×AGL(1,𝔽11)
HallC3×C11 ⋊ C5×D53
SylowC11 ⋊ C3×C5×D53

Subgroups

subgroupG/H
center, hypercenterC3C53⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC11×C53C2×C3×C5
FrattiniC1G
Fitting, socleC3×C11×C53C2×C5
LCSG ▷ C11×C53
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1749

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×D53×AGL(1,𝔽11), D3×C53⋊AGL(1,𝔽11), D159⋊AGL(1,𝔽11), …
maximal normal subgroup ofC3×D53×AGL(1,𝔽11), D3×C53⋊AGL(1,𝔽11), D159⋊AGL(1,𝔽11), …
maximal quotient ofC3×(C11⋊C5)⋊Dic53, C2×C3×C53⋊AGL(1,𝔽11)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17490, 20);