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C23×AGL(1,𝔽11) #11725042

order880
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C26

Aliases

direct productC23×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C23×C5)
unambiguous semidirect product(C11⋊C5)⋊C24
unambiguous semidirect product(C2×C11⋊C5)⋊C23
unambiguous semidirect product(C23×D11)⋊C5

Splittings

Fitting, socleC23×C11 ⋊ C2×C5
derived, SylowC11 ⋊ C24×C5
HallC23×D11 ⋊ C5
HallC11⋊C5 ⋊ C24

Subgroups

subgroupG/H
center, hypercenterC23AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C24×C5
FrattiniC1G
Fitting, socleC23×C11C2×C5
LCSG ▷ C11
UCSC1 ◁ C23

268 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 ofC22⋊C4×AGL(1,𝔽11), #66935⋊C5, C2×((C2×D11)⋊C4)⋊C5, …
maximal normal subgroup ofC22⋊C4×AGL(1,𝔽11), #66935⋊C5, C2×((C2×D11)⋊C4)⋊C5, …
maximal quotient ofC22×(C11⋊C5)⋊Q8, C22×C4×AGL(1,𝔽11), C22×C4⋊AGL(1,𝔽11), …
automorphism group ofC8×D11, #4313, C3×C11⋊C8, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(880, 210);