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Cayley diagram

C4×C11 #191

order44
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C22×C5 (order 20) · Inn(G) = C1 · Out(G) = C22×C5
holomorphG ⋊ Aut(G) = D4×AGL(1,𝔽11)
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC44
abelianC4×C11

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C2×C11
socle, prime radicalC2×C11C2
LCSG ▷ C1
UCSC1 ◁ G

6 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 1 generator on 15 points:

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

Conjugacy classes & character table

44 conjugacy classes — view the full character table.

Relationships

center ofC11×M16, C11×#41, C11×C3⋊C8, …
derived subgroup of#4314, D88, Dic44, …
Frattini subgroup ofC121⋊C8, C8×C121, Dic484, …
Fitting subgroup ofC11⋊C8, Dic22, C4×D11, …
maximal subgroup ofC11⋊C8, C8×C11, Dic22, …
maximal normal subgroup ofC11⋊C8, C8×C11, Dic22, …
maximal quotient ofC8×C11, C2×C4×C11, C11×Dic3, …
outer automorphism group ofD89, C5×D23, D115

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(44, 2);