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C7×C3⋊(C5⋊AGL(1,𝔽11)) #26040493

order11550
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C3⋊(C5⋊AGL(1,𝔽11))
unambiguous semidirect productC3⋊(C7×C5⋊AGL(1,𝔽11))
unambiguous semidirect productC5⋊(C7×C3⋊AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(C7×D15)
unambiguous semidirect productD165⋊(C5×C7)
unambiguous semidirect product(C7×D165)⋊C5

Splittings

Fitting, socleC3×C5×C7×C11 ⋊ C2×C5
derivedC3×C5×C11 ⋊ C2×C5×C7
HallC3×C5×C7×C11⋊C5 ⋊ C2
HallC5×C7×C11⋊C5 ⋊ D3
HallC3×C5×C11⋊C5 ⋊ C2×C7
HallC5×C11⋊C5 ⋊ D3×C7
HallC3×C7×C11 ⋊ C5×D5
HallC7×C11 ⋊ C5×D15
HallC3×C11 ⋊ C5×C7×D5
HallC3×C7 ⋊ C5⋊AGL(1,𝔽11)
SylowC11 ⋊ C5×C7×D15
SylowC3 ⋊ C7×C5⋊AGL(1,𝔽11)

Subgroups

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

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

420 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×D15×AGL(1,𝔽11), D7×C3⋊(C5⋊AGL(1,𝔽11)), (C7⋊AGL(1,𝔽11))⋊D15, …
maximal normal subgroup ofC7×D15×AGL(1,𝔽11), D7×C3⋊(C5⋊AGL(1,𝔽11)), (C7⋊AGL(1,𝔽11))⋊D15, …
maximal quotient ofC7×C3⋊((C11⋊C5)⋊Dic5), C2×C7×C3⋊(C5⋊AGL(1,𝔽11)), C7×C5⋊(C9⋊AGL(1,𝔽11)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11550, 57);