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C2×C3⋊(C13⋊AGL(1,𝔽11)) #22575109

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

Aliases

direct productC2×C3⋊(C13⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C3)⋊(C13⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C13)⋊(C3⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C11⋊C5)⋊D39
unambiguous semidirect product(C2×D429)⋊C5

Splittings

Fitting, socleC2×C3×C11×C13 ⋊ C2×C5
derived, HallC3×C11×C13 ⋊ C22×C5
HallC3×C13×C11⋊C5 ⋊ C22
HallC2×D429 ⋊ C5
HallC13×C11⋊C5 ⋊ C2×D3
HallC3×C11⋊C5 ⋊ C2×D13
HallC11×C13 ⋊ C2×C5×D3
HallC11⋊C5 ⋊ C2×D39
HallC3×C13 ⋊ C2×AGL(1,𝔽11)
HallC3×C11 ⋊ C2×C5×D13
SylowC13 ⋊ C2×C3⋊AGL(1,𝔽11)
SylowC11 ⋊ C2×C5×D39
SylowC3 ⋊ C2×C13⋊AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC2C3⋊(C13⋊AGL(1,𝔽11))
commutator, hypocenterC3×C11×C13C22×C5
FrattiniC1G
Fitting, socleC2×C3×C11×C13C2×C5
LCSG ▷ C3×C11×C13
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

288 conjugacy classes — view the full character table.

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 81);