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C2×C4×AGL(1,𝔽11) #11724947

order880
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC2×C4×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C2×C4×C5)
unambiguous semidirect product(C2×C4×D11)⋊C5

Splittings

FittingC2×C4×C11 ⋊ C2×C5
derived, SylowC11 ⋊ C22×C4×C5
HallC2×C4×D11 ⋊ C5
HallC11⋊C5 ⋊ C22×C4

Subgroups

subgroupG/H
center, hypercenterC2×C4AGL(1,𝔽11)
commutator, hypocenterC11C22×C4×C5
FrattiniC2C22×AGL(1,𝔽11)
FittingC2×C4×C11C2×C5
socleC22×C11C22×C5
prime radicalC22×AGL(1,𝔽11)C2
cosocleC2×C11C23×C5
LCSG ▷ C11
UCSC1 ◁ C2×C4

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 88

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×AGL(1,𝔽11))⋊C8, C42×AGL(1,𝔽11), #66925⋊C5, …
maximal normal subgroup of(C2×AGL(1,𝔽11))⋊C8, C42×AGL(1,𝔽11), #66925⋊C5, …
maximal quotient ofC4×(C11⋊C5)⋊Q8, C42×AGL(1,𝔽11), #66925⋊C5, …
automorphism group ofC11⋊C16, C5×Dic11, C2×C5×D11, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(880, 115);