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C72×C3⋊AGL(1,𝔽11) #30633520

order16170
isoclinismisoclinic class of C3⋊AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C2×C5×C72 · Schur multiplier (H2) = C7

Aliases

direct productC72×C3⋊AGL(1,𝔽11)
unambiguous semidirect productC3⋊(C72×AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(D3×C72)
unambiguous semidirect productD33⋊(C5×C72)
unambiguous semidirect product(C7×D33)⋊(C5×C7)
unambiguous semidirect product(C72×D33)⋊C5

Splittings

Fitting, socle, HallC3×C72×C11 ⋊ C2×C5
derived, HallC3×C11 ⋊ C2×C5×C72
HallC3×C72×C11⋊C5 ⋊ C2
HallC72×D33 ⋊ C5
HallC72×C11⋊C5 ⋊ D3
HallC72×C11 ⋊ C5×D3
HallC3×C11⋊C5 ⋊ C2×C72
HallC3×C72 ⋊ AGL(1,𝔽11)
HallD33 ⋊ C5×C72
HallC11⋊C5 ⋊ D3×C72
SylowC11 ⋊ C5×D3×C72
SylowC3 ⋊ C72×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC72C3⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC3×C11C2×C5×C72
FrattiniC1G
Fitting, socleC3×C72×C11C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C72

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1617

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD3×C72×AGL(1,𝔽11), C7×D7×C3⋊AGL(1,𝔽11), C7×D21⋊AGL(1,𝔽11), …
maximal normal subgroup ofD3×C72×AGL(1,𝔽11), C7×D7×C3⋊AGL(1,𝔽11), C7×D21⋊AGL(1,𝔽11), …
maximal quotient ofC72×C3⋊(Dic11⋊C5), C2×C72×C3⋊AGL(1,𝔽11)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 65);