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C2×(C13⋊C3)⋊AGL(1,𝔽11) #22575069

order8580
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×(C13⋊C3)⋊AGL(1,𝔽11)
unambiguous semidirect product(C2×C13⋊C3)⋊AGL(1,𝔽11)
unambiguous semidirect product(C2×C11⋊C5)⋊(D13⋊C3)
unambiguous semidirect product(C2×C11⋊(D13⋊C3))⋊C5
unambiguous semidirect product(C2×C13⋊AGL(1,𝔽11))⋊C3

Splittings

Fitting, socleC2×C11×C13 ⋊ C2×C3×C5
derived, HallC11×C13 ⋊ C22×C3×C5
HallC2×C13⋊AGL(1,𝔽11) ⋊ C3
HallC13⋊C3×C11⋊C5 ⋊ C22
HallC2×C11⋊(D13⋊C3) ⋊ C5
HallC13×C11⋊C5 ⋊ C22×C3
HallC2×D143 ⋊ C3×C5
HallC11×C13⋊C3 ⋊ C22×C5
HallC11⋊C5 ⋊ C2×D13⋊C3
HallC13⋊C3 ⋊ C2×AGL(1,𝔽11)
SylowC13 ⋊ C2×C3×AGL(1,𝔽11)
SylowC11 ⋊ C2×C5×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2(C13⋊C3)⋊AGL(1,𝔽11)
commutator, hypocenterC11×C13C22×C3×C5
FrattiniC1G
Fitting, socleC2×C11×C13C2×C3×C5
LCSG ▷ C11×C13
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

94 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×(C13⋊C3)⋊AGL(1,𝔽11), C2×C3×(C13⋊C3)⋊AGL(1,𝔽11), C2×C3⋊((C13⋊C3)⋊AGL(1,𝔽11))
maximal normal subgroup ofC2×C3×(C13⋊C3)⋊AGL(1,𝔽11)
maximal quotient ofC2×(C11⋊C5)⋊(D13⋊C9), D3×(C13⋊C3)⋊AGL(1,𝔽11), C2×C3×(C13⋊C3)⋊AGL(1,𝔽11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 41);