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Cayley diagram

C17 #43

order17
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C16 (order 16) · Inn(G) = C1 · Out(G) = C16
holomorphG ⋊ Aut(G) = AGL(1,𝔽17)
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC17

Subgroups

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

2 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 17
transitive degreeμt(G) = 17

A minimal faithful permutation representation — 1 generator on 17 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)

Conjugacy classes & character table

17 conjugacy classes — view the full character table.

Relationships

center ofD3×C17, D5×C17, A4×C17, …
derived subgroup ofD17, Dic17, #595, …
Frattini subgroup ofC289, D289, C2×C289, …
Fitting subgroup ofD17, #595, #3633, …
socle ofD17, #595, #3633, …
maximal subgroup ofD17, C2×C17, C3×C17, …
maximal normal subgroup ofD17, C2×C17, C3×C17, …
maximal quotient ofC2×C17, C3×C17, C5×C17, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17, 1);