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C13×C43 #10587828

order559
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C2×C32×C4×C7 (order 504) · Inn(G) = C1 · Out(G) = C2×C32×C4×C7
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC559
abelianC13×C43

Subgroups

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

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 56
transitive degreeμt(G) = 559

A minimal faithful permutation representation — 1 generator on 56 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)

Conjugacy classes & character table

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

Relationships

center ofD3×C13×C43, C13×D13×C43, C13×D15×C43, …
derived subgroup ofD559, #13131975, #13131976, …
Fitting subgroup ofD13×C43, C13×D43, D559, …
socle ofD13×C43, C13×D43, D559, …
maximal subgroup ofD13×C43, C13×D43, D559, …
maximal normal subgroup ofD13×C43, C13×D43, D559, …
maximal quotient ofC2×C13×C43, C3×C13×C43, C5×C13×C43, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(559, 1);