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C23×C37 #11719971

order851
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C2×C4×C9×C11 (order 792) · Inn(G) = C1 · Out(G) = C2×C4×C9×C11
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC851
abelianC23×C37

Subgroups

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

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 60
transitive degreeμt(G) = 851

A minimal faithful permutation representation — 1 generator on 60 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)

Conjugacy classes & character table

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

Relationships

center ofD9×C23×C37, C3⋊D3×C23×C37, AGL(1,𝔽5)×C23×C37, …
derived subgroup ofD851, Dic851, C23⋊#3866, …
Fitting subgroup ofC37×D23, C23×D37, D851, …
socle ofC37×D23, C23×D37, D851, …
maximal subgroup ofC37×D23, C23×D37, D851, …
maximal normal subgroup ofC37×D23, C23×D37, D851, …
maximal quotient ofC2×C23×C37, C3×C23×C37, C5×C23×C37, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(851, 1);