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C3×C5⋊(C7⋊AGL(1,𝔽11)) #26040487

order11550
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5⋊(C7⋊AGL(1,𝔽11))
unambiguous semidirect productC5⋊(C3×C7⋊AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(C3×D35)
unambiguous semidirect product(C3×D385)⋊C5

Splittings

Fitting, socleC3×C5×C7×C11 ⋊ C2×C5
derivedC5×C7×C11 ⋊ C2×C3×C5
HallC3×C5×C7×C11⋊C5 ⋊ C2
HallC5×C7×C11⋊C5 ⋊ C2×C3
HallC3×C5×C11⋊C5 ⋊ D7
HallC5×C11⋊C5 ⋊ C3×D7
HallC3×C7×C11 ⋊ C5×D5
HallC7×C11 ⋊ C3×C5×D5
HallC3×C11 ⋊ C5×D35
HallC3×C7 ⋊ C5⋊AGL(1,𝔽11)
SylowC11 ⋊ C3×C5×D35
SylowC7 ⋊ C3×C5⋊AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC3C5⋊(C7⋊AGL(1,𝔽11))
commutator, cosocle, hypocenterC5×C7×C11C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C11C2×C5
LCSG ▷ C5×C7×C11
UCSC1 ◁ C3

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

390 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D35×AGL(1,𝔽11), C3×D7×C5⋊AGL(1,𝔽11), C3×D5×C7⋊AGL(1,𝔽11), …
maximal normal subgroup ofC3×D35×AGL(1,𝔽11), C3×D7×C5⋊AGL(1,𝔽11), C3×D5×C7⋊AGL(1,𝔽11), …
maximal quotient ofC3×C7⋊((C11⋊C5)⋊Dic5), C2×C3×C5⋊(C7⋊AGL(1,𝔽11)), C9×C5⋊(C7⋊AGL(1,𝔽11)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11550, 51);