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Cayley diagram

C4×AGL(1,𝔽11) #89155

order440
isoclinismisoclinic class of AGL(1,𝔽11)
automorphismAut(G) = C22×AGL(1,𝔽11) (order 440) · Inn(G) = AGL(1,𝔽11) · Out(G) = C22
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2

Aliases

direct productC4×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C4×C5)
unambiguous semidirect product(C4×D11)⋊C5

Splittings

FittingC4×C11 ⋊ C2×C5
derived, SylowC11 ⋊ C2×C4×C5
HallC4×D11 ⋊ C5
HallC11⋊C5 ⋊ C2×C4

Subgroups

subgroupG/H
center, hypercenterC4AGL(1,𝔽11)
commutator, hypocenterC11C2×C4×C5
FrattiniC2C2×AGL(1,𝔽11)
FittingC4×C11C2×C5
socle, cosocleC2×C11C22×C5
prime radicalC2×AGL(1,𝔽11)C2
LCSG ▷ C11
UCSC1 ◁ C4

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 15
transitive degreeμt(G) = 44

A minimal faithful permutation representation — 2 generators on 15 points:

(6,10,11,9,14,7,8,15,12,13);(1,2,3,4)(5,6,9,14,8,11,15,10,13,12,7)

Conjugacy classes & character table

44 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC8×AGL(1,𝔽11), #4313⋊C5, C2×C4×AGL(1,𝔽11), …
maximal normal subgroup ofC8×AGL(1,𝔽11), #4313⋊C5, C2×C4×AGL(1,𝔽11), …
maximal quotient ofC8×AGL(1,𝔽11), #4313⋊C5, C4×Dic11⋊C5, …
automorphism group ofC5×D11

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(440, 8);