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C3×C7×C7⋊AGL(1,𝔽11) #30633516

order16170
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×C7⋊AGL(1,𝔽11)
unambiguous semidirect product(C11⋊C5)⋊(C3×C7×D7)
unambiguous semidirect product(C3×D77)⋊(C5×C7)
unambiguous semidirect product(C3×C7×D77)⋊C5

Splittings

Fitting, socle, HallC3×C72×C11 ⋊ C2×C5
derivedC7×C11 ⋊ C2×C3×C5×C7
HallC3×C72×C11⋊C5 ⋊ C2
HallC3×C7×D77 ⋊ C5
HallC72×C11⋊C5 ⋊ C2×C3
HallC7×D77 ⋊ C3×C5
HallC72×C11 ⋊ C2×C3×C5
HallC3×C11⋊C5 ⋊ C7×D7
HallC3×C72 ⋊ AGL(1,𝔽11)
HallC11⋊C5 ⋊ C3×C7×D7
SylowC72 ⋊ C3×AGL(1,𝔽11)
HallC3×C11 ⋊ C5×C7×D7
SylowC11 ⋊ C3×C5×C7×D7

Subgroups

subgroupG/H
center, hypercenterC3×C7C7⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC7×C11C2×C3×C5×C7
FrattiniC1G
Fitting, socleC3×C72×C11C2×C5
LCSG ▷ C7×C11
UCSC1 ◁ C3×C7

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 462

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×C7×D7×AGL(1,𝔽11), C3×D7×C7⋊AGL(1,𝔽11), C3×(C7⋊D7)⋊AGL(1,𝔽11), …
maximal normal subgroup ofC3×C7×D7×AGL(1,𝔽11), C3×D7×C7⋊AGL(1,𝔽11), C3×(C7⋊D7)⋊AGL(1,𝔽11), …
maximal quotient ofC3×C7×C7⋊(Dic11⋊C5), C2×C3×C7×C7⋊AGL(1,𝔽11)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 61);