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AGL(1,𝔽11)×#3861 #30633506

order16170
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productAGL(1,𝔽11)×#3861
unambiguous semidirect productD11⋊(C5×#3861)
unambiguous semidirect product(C11⋊C5)⋊(C2×#3861)
unambiguous semidirect product(D11×#3861)⋊C5

Splittings

Fitting, socle, derived, HallC72×C11 ⋊ C2×C3×C5
HallC11⋊C5×#3861 ⋊ C2
HallC72×AGL(1,𝔽11) ⋊ C3
HallD11×#3861 ⋊ C5
HallC72×C11⋊C5 ⋊ C2×C3
HallC11×#3861 ⋊ C2×C5
HallC72×D11 ⋊ C3×C5
HallC11⋊C5 ⋊ C2×#3861
SylowC72 ⋊ C3×AGL(1,𝔽11)
HallD11 ⋊ C5×#3861
SylowC11 ⋊ C2×C5×#3861

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC72×C11C2×C3×C5
LCSG ▷ C72×C11
UCSC1

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 539

Conjugacy classes & character table

209 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽11)×#64424, AGL(1,𝔽11)×#64423, C2×AGL(1,𝔽11)×#3861
maximal normal subgroup ofAGL(1,𝔽11)×#64424, AGL(1,𝔽11)×#64423, C2×AGL(1,𝔽11)×#3861
maximal quotient of#3861×Dic11⋊C5, C2×AGL(1,𝔽11)×#3861

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 51);