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Cayley diagram

C121 #1238

order121
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C2×C5×C11 (order 110) · Inn(G) = C1 · Out(G) = C2×C5×C11
holomorphG ⋊ Aut(G) = #72230792
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC121

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, socle, prime radical, cosocleC11C11
LCSG ▷ C1
UCSC1 ◁ G
LECSG ▷ C11 ▷ C1

3 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 121
transitive degreeμt(G) = 121

A minimal faithful permutation representation — 1 generator on 121 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121)

Conjugacy classes & character table

121 conjugacy classes — view the full character table.

Relationships

center ofD3×C121, D5×C121, A4×C121, …
derived subgroup ofD121, Dic121, C2×D121, …
Frattini subgroup ofC1331, C11×C1331, C1331⋊C11, …
Fitting subgroup ofD121, C121⋊C5, D121⋊C5, …
maximal subgroup ofD121, C2×C121, C3×C121, …
maximal normal subgroup ofD121, C2×C121, C3×C121, …
maximal quotient ofC2×C121, C3×C121, C5×C121, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(121, 1);