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Cayley diagram

C11×C17 #4419

order187
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C2×C5×C16 (order 160) · Inn(G) = C1 · Out(G) = C2×C5×C16
holomorphG ⋊ Aut(G) = AGL(1,𝔽11)×AGL(1,𝔽17)
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC187
abelianC11×C17

Subgroups

subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 187

A minimal faithful permutation representation — 1 generator on 28 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28)

Conjugacy classes & character table

187 conjugacy classes — view the full character table.

Relationships

center ofD3×C11×C17, D5×C11×C17, C11×A4×C17, …
derived subgroup ofD187, Dic187, C11⋊#595, …
Frattini subgroup ofC121×C289
Fitting subgroup ofC17×D11, C11×D17, D187, …
socle ofC17×D11, C11×D17, D187, …
maximal subgroup ofC17×D11, C11×D17, D187, …
maximal normal subgroup ofC17×D11, C11×D17, D187, …
maximal quotient ofC2×C11×C17, C3×C11×C17, C5×C11×C17, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(187, 1);