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C2×C3×C7⋊AGL(1,𝔽11) #17987667

order4620
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C7⋊AGL(1,𝔽11)
unambiguous semidirect product(C2×C11⋊C5)⋊(C3×D7)
unambiguous semidirect product(C2×C3×D77)⋊C5

Splittings

Fitting, socleC2×C3×C7×C11 ⋊ C2×C5
derived, HallC7×C11 ⋊ C22×C3×C5
HallC3×C7×C11⋊C5 ⋊ C22
HallC2×C3×D77 ⋊ C5
HallC7×C11⋊C5 ⋊ C22×C3
HallC2×D77 ⋊ C3×C5
HallC3×C7×C11 ⋊ C22×C5
HallC3×C11⋊C5 ⋊ C2×D7
HallC11⋊C5 ⋊ C2×C3×D7
HallC3×C11 ⋊ C2×C5×D7
HallC3×C7 ⋊ C2×AGL(1,𝔽11)
SylowC11 ⋊ C2×C3×C5×D7
SylowC7 ⋊ C2×C3×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC2×C3C7⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC7×C11C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C7×C11C2×C5
LCSG ▷ C7×C11
UCSC1 ◁ C2×C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 462

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×(C11⋊C5)⋊(D7⋊C9), C2×C9×C7⋊AGL(1,𝔽11), C2×C3×ΓL(1,𝔽8)⋊AGL(1,𝔽11), …
maximal normal subgroup ofC2×(C11⋊C5)⋊(D7⋊C9), C2×C9×C7⋊AGL(1,𝔽11), C2×C3×ΓL(1,𝔽8)⋊AGL(1,𝔽11), …
maximal quotient ofC2×C9×C7⋊AGL(1,𝔽11), C3×D3×C7⋊AGL(1,𝔽11), C2×C32×C7⋊AGL(1,𝔽11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4620, 64);