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C3×C5×C7⋊AGL(1,𝔽11) #26040483

order11550
automorphism?
homologyAbelianization (H1) = C2×C3×C52 · Schur multiplier (H2) = C5

Aliases

direct productC3×C5×C7⋊AGL(1,𝔽11)
unambiguous semidirect product(C11⋊C5)⋊(C3×C5×D7)
unambiguous semidirect product(C3×D77)⋊C52
unambiguous semidirect product(C3×C5×D77)⋊C5

Splittings

Fitting, socleC3×C5×C7×C11 ⋊ C2×C5
derived, HallC7×C11 ⋊ C2×C3×C52
HallC3×C5×C7×C11⋊C5 ⋊ C2
HallC5×C7×C11⋊C5 ⋊ C2×C3
HallC3×C5×C11⋊C5 ⋊ D7
HallC3×D77 ⋊ C52
HallC5×C11⋊C5 ⋊ C3×D7
HallC3×C7×C11 ⋊ C2×C52
HallD77 ⋊ C3×C52
HallC3×C11 ⋊ C52×D7
HallC3×C7 ⋊ C5×AGL(1,𝔽11)
SylowC11 ⋊ C3×C52×D7
SylowC7 ⋊ C3×C5×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC3×C5C7⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC7×C11C2×C3×C52
FrattiniC1G
Fitting, socleC3×C5×C7×C11C2×C5
LCSG ▷ C7×C11
UCSC1 ◁ C3×C5

128 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

480 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C5×D7×AGL(1,𝔽11), C3×D5×C7⋊AGL(1,𝔽11), C3×D35⋊AGL(1,𝔽11), …
maximal normal subgroup ofC3×C5×D7×AGL(1,𝔽11), C3×D5×C7⋊AGL(1,𝔽11), C3×D35⋊AGL(1,𝔽11), …
maximal quotient ofC3×C5×C7⋊(Dic11⋊C5), C2×C3×C5×C7⋊AGL(1,𝔽11), C5×C9×C7⋊AGL(1,𝔽11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11550, 47);