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C19×C59 #11765487

order1121
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C22×C9×C29 (order 1044) · Inn(G) = C1 · Out(G) = C22×C9×C29
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC1121
abelianC19×C59

Subgroups

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

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 78
transitive degreeμt(G) = 1121

A minimal faithful permutation representation — 1 generator on 78 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)

Conjugacy classes & character table

1121 conjugacy classes. The character table is too large to display.

Relationships

center ofD7×C19×C59, C19×AGL(1,𝔽5)×C59, C19×ΓL(1,𝔽8)×C59, …
derived subgroup ofD1121, C7×D1121, C5×Dic1121, …
Fitting subgroup ofD19×C59, C19×D59, D1121, …
socle ofD19×C59, C19×D59, D1121, …
maximal subgroup ofD19×C59, C19×D59, D1121, …
maximal normal subgroup ofD19×C59, C19×D59, D1121, …
maximal quotient ofC2×C19×C59, C3×C19×C59, C13×C19×C59, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1121, 1);