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C11×C71 #11715971

order781
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C22×C52×C7 (order 700) · Inn(G) = C1 · Out(G) = C22×C52×C7
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC781
abelianC11×C71

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) = 781

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

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

Relationships

center ofC11×D9×C71, C11×C3⋊D3×C71, C11×AGL(1,𝔽5)×C71, …
derived subgroup ofD781, Dic781, D11×D71, …
Fitting subgroup ofD11×C71, C11×D71, D781, …
socle ofD11×C71, C11×D71, D781, …
maximal subgroup ofD11×C71, C11×D71, D781, …
maximal normal subgroup ofD11×C71, C11×D71, D781, …
maximal quotient ofC2×C11×C71, C3×C11×C71, C5×C11×C71, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(781, 1);