Finite Group Databasebeta

← Prev (#30633517) Next (#30633519) →

C3×C7⋊(C7⋊AGL(1,𝔽11)) #30633518

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

Aliases

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

Splittings

Fitting, socle, HallC3×C72×C11 ⋊ C2×C5
derived, HallC72×C11 ⋊ C2×C3×C5
HallC3×C72×C11⋊C5 ⋊ C2
HallC3×C7⋊D77 ⋊ C5
HallC72×C11⋊C5 ⋊ C2×C3
HallC7⋊D77 ⋊ 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, hypercenterC3C7⋊(C7⋊AGL(1,𝔽11))
commutator, cosocle, hypocenterC72×C11C2×C3×C5
FrattiniC1G
Fitting, socleC3×C72×C11C2×C5
LCSG ▷ C72×C11
UCSC1 ◁ C3

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1617

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×D7×C7⋊AGL(1,𝔽11), C3×C7⋊D7×AGL(1,𝔽11), D21⋊(C7⋊AGL(1,𝔽11)), …
maximal normal subgroup ofC3×D7×C7⋊AGL(1,𝔽11), C3×C7⋊D7×AGL(1,𝔽11), D21⋊(C7⋊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, 63);