Finite Group Databasebeta

← Prev (#26014365) Next (#26014367) →

C2×C3⋊(C17⋊AGL(1,𝔽11)) #26014366

order11220
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3⋊(C17⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C3)⋊(C17⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C17)⋊(C3⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C11⋊C5)⋊D51
unambiguous semidirect product(C2×D561)⋊C5

Splittings

Fitting, socleC2×C3×C11×C17 ⋊ C2×C5
derived, HallC3×C11×C17 ⋊ C22×C5
HallC3×C17×C11⋊C5 ⋊ C22
HallC2×D561 ⋊ C5
HallC17×C11⋊C5 ⋊ C2×D3
HallC11×C17 ⋊ C2×C5×D3
HallC3×C11⋊C5 ⋊ C2×D17
HallC11⋊C5 ⋊ C2×D51
HallC3×C17 ⋊ C2×AGL(1,𝔽11)
HallC3×C11 ⋊ C2×C5×D17
SylowC17 ⋊ C2×C3⋊AGL(1,𝔽11)
SylowC11 ⋊ C2×C5×D51
SylowC3 ⋊ C2×C17⋊AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC2C3⋊(C17⋊AGL(1,𝔽11))
commutator, cosocle, hypocenterC3×C11×C17C22×C5
FrattiniC1G
Fitting, socleC2×C3×C11×C17C2×C5
LCSG ▷ C3×C11×C17
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

372 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C9⋊(C17⋊AGL(1,𝔽11)), D3×C3⋊(C17⋊AGL(1,𝔽11)), C2×C3×C3⋊(C17⋊AGL(1,𝔽11)), …
maximal normal subgroup ofC2×C3×C3⋊(C17⋊AGL(1,𝔽11))
maximal quotient ofC2×C9⋊(C17⋊AGL(1,𝔽11)), D3×C3⋊(C17⋊AGL(1,𝔽11)), C2×C3×C3⋊(C17⋊AGL(1,𝔽11)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11220, 42);