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C3⋊(C5⋊(C7⋊AGL(1,𝔽11))) #26040495

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

Aliases

unambiguous semidirect productC3⋊(C5⋊(C7⋊AGL(1,𝔽11)))
unambiguous semidirect productC5⋊(C3⋊(C7⋊AGL(1,𝔽11)))
unambiguous semidirect productC7⋊(C3⋊(C5⋊AGL(1,𝔽11)))
unambiguous semidirect product(C11⋊C5)⋊D105
unambiguous semidirect productD1155⋊C5

Splittings

Fitting, socle, derivedC3×C5×C7×C11 ⋊ C2×C5
HallC3×C5×C7×C11⋊C5 ⋊ C2
HallC5×C7×C11⋊C5 ⋊ D3
HallC3×C5×C11⋊C5 ⋊ D7
HallC5×C11⋊C5 ⋊ D21
HallC3×C7×C11 ⋊ C5×D5
HallC7×C11 ⋊ C5×D15
HallC3×C11 ⋊ C5×D35
HallC3×C7 ⋊ C5⋊AGL(1,𝔽11)
SylowC11 ⋊ C5×D105
SylowC7 ⋊ C3⋊(C5⋊AGL(1,𝔽11))
SylowC3 ⋊ C5⋊(C7⋊AGL(1,𝔽11))

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C7×C11C2×C5
LCSG ▷ C3×C5×C7×C11
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,5,3,5,7,11|c^a=c^2,d^a=d^4,e^a=e^6,f^a=f^10,f^b=f^4

Conjugacy classes & character table

375 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽11)×D105, D7×C3⋊(C5⋊AGL(1,𝔽11)), D15×C7⋊AGL(1,𝔽11), …
maximal normal subgroup ofAGL(1,𝔽11)×D105, D7×C3⋊(C5⋊AGL(1,𝔽11)), D15×C7⋊AGL(1,𝔽11), …
maximal quotient ofC3⋊(C7⋊((C11⋊C5)⋊Dic5)), C2×C3⋊(C5⋊(C7⋊AGL(1,𝔽11))), C5⋊(C7⋊(C9⋊AGL(1,𝔽11))), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11550, 59);