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C17×C41 #10621978

order697
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C5×C8×C16 (order 640) · Inn(G) = C1 · Out(G) = C5×C8×C16
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC697
abelianC17×C41

Subgroups

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

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 58
transitive degreeμt(G) = 697

A minimal faithful permutation representation — 1 generator on 58 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58)

Conjugacy classes & character table

697 conjugacy classes. The character table is too large to display.

Relationships

center ofD3×C17×C41, C17×AGL(1,𝔽5)×C41, C17×ΓL(1,𝔽8)×C41, …
derived subgroup ofD697, Dic697, #14584032, …
Fitting subgroup ofD17×C41, C17×D41, D697, …
socle ofD17×C41, C17×D41, D697, …
maximal subgroup ofD17×C41, C17×D41, D697, …
maximal normal subgroup ofD17×C41, C17×D41, D697, …
maximal quotient ofC2×C17×C41, C3×C17×C41, C5×C17×C41, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(697, 1);