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C7×C3⋊(C7⋊AGL(1,𝔽11)) #30633522

order16170
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C3⋊(C7⋊AGL(1,𝔽11))
unambiguous semidirect productC3⋊(C7×C7⋊AGL(1,𝔽11))
unambiguous semidirect productC7⋊(C7×C3⋊AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(C7×D21)
unambiguous semidirect productD231⋊(C5×C7)
unambiguous semidirect product(C7×D231)⋊C5

Splittings

Fitting, socle, HallC3×C72×C11 ⋊ C2×C5
derivedC3×C7×C11 ⋊ C2×C5×C7
HallC3×C72×C11⋊C5 ⋊ C2
HallC7×D231 ⋊ C5
HallC72×C11⋊C5 ⋊ D3
HallC72×C11 ⋊ C5×D3
HallC3×C11⋊C5 ⋊ C7×D7
HallC3×C72 ⋊ AGL(1,𝔽11)
HallC11⋊C5 ⋊ C7×D21
SylowC72 ⋊ C3⋊AGL(1,𝔽11)
HallC3×C11 ⋊ C5×C7×D7
SylowC11 ⋊ C5×C7×D21
SylowC3 ⋊ C7×C7⋊AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC7C3⋊(C7⋊AGL(1,𝔽11))
commutator, cosocle, hypocenterC3×C7×C11C2×C5×C7
FrattiniC1G
Fitting, socleC3×C72×C11C2×C5
LCSG ▷ C3×C7×C11
UCSC1 ◁ C7

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 462

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC7×D21×AGL(1,𝔽11), C7×D7×C3⋊AGL(1,𝔽11), D3×C7×C7⋊AGL(1,𝔽11), …
maximal normal subgroup ofC7×D21×AGL(1,𝔽11), C7×D7×C3⋊AGL(1,𝔽11), D3×C7×C7⋊AGL(1,𝔽11), …
maximal quotient ofC7×C3⋊(C7⋊(Dic11⋊C5)), C2×C7×C3⋊(C7⋊AGL(1,𝔽11))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 67);