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AGL(1,𝔽11)2 #27130877

order12100
automorphism?
homologyAbelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productAGL(1,𝔽11)2
unambiguous semidirect product(#11925892⋊C2)⋊C5
unambiguous semidirect product(#11925896⋊C2)⋊C5
unambiguous semidirect product(#11925894⋊C2)⋊C5
unambiguous semidirect product(D11×AGL(1,𝔽11))⋊C5
unambiguous semidirect product(C11⋊C5×AGL(1,𝔽11))⋊C2

Splittings

Fitting, socle, derived, SylowC112 ⋊ C22×C52
HallC11⋊C52 ⋊ C22
HallD112 ⋊ C52

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC112C22×C52
LCSG ▷ C112
UCSC1

164 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

121 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×AGL(1,𝔽11)2, AGL(1,𝔽11)×C3⋊AGL(1,𝔽11), (C3⋊AGL(1,𝔽11))⋊AGL(1,𝔽11), …
maximal normal subgroup ofC3×AGL(1,𝔽11)2, C2×AGL(1,𝔽11)2
maximal quotient ofC3×AGL(1,𝔽11)2, AGL(1,𝔽11)×C3⋊AGL(1,𝔽11), (C3⋊AGL(1,𝔽11))⋊AGL(1,𝔽11), …
holomorph ofAGL(1,𝔽11)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12100, 156);