Finite Group Databasebeta

← Prev (#23780279) Next (#23780281) →

C2×C47⋊AGL(1,𝔽11) #23780280

order10340
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C47⋊AGL(1,𝔽11)
unambiguous semidirect product(C2×C47)⋊AGL(1,𝔽11)
unambiguous semidirect product(C2×C11⋊C5)⋊D47
unambiguous semidirect product(C2×D517)⋊C5

Splittings

Fitting, socleC2×C11×C47 ⋊ C2×C5
derived, HallC11×C47 ⋊ C22×C5
HallC47×C11⋊C5 ⋊ C22
HallC2×D517 ⋊ C5
HallC11⋊C5 ⋊ C2×D47
SylowC47 ⋊ C2×AGL(1,𝔽11)
SylowC11 ⋊ C2×C5×D47

Subgroups

subgroupG/H
center, hypercenterC2C47⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC11×C47C22×C5
FrattiniC1G
Fitting, socleC2×C11×C47C2×C5
LCSG ▷ C11×C47
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

344 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C47⋊AGL(1,𝔽11), C2×C3×C47⋊AGL(1,𝔽11), C2×C3⋊(C47⋊AGL(1,𝔽11))
maximal normal subgroup ofC2×C3×C47⋊AGL(1,𝔽11)
maximal quotient ofD3×C47⋊AGL(1,𝔽11), C2×C3×C47⋊AGL(1,𝔽11), C2×C3⋊(C47⋊AGL(1,𝔽11))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10340, 16);