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C29×C53 #13095283

order1537
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C42×C7×C13 (order 1456) · Inn(G) = C1 · Out(G) = C42×C7×C13
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC1537
abelianC29×C53

Subgroups

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

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 82
transitive degreeμt(G) = 1537

A minimal faithful permutation representation — 1 generator on 82 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)(30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82)

Conjugacy classes & character table

1537 conjugacy classes. The character table is too large to display.

Relationships

center ofD5×C29×C53, A4×C29×C53, D7×C29×C53, …
derived subgroup ofD1537, C5×D1537, C3×Dic1537, …
Fitting subgroup ofC53×D29, C29×D53, D1537, …
socle ofC53×D29, C29×D53, D1537, …
maximal subgroup ofC53×D29, C29×D53, D1537, …
maximal normal subgroup ofC53×D29, C29×D53, D1537, …
maximal quotient ofC2×C29×C53, C3×C29×C53, C11×C29×C53, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1537, 1);