Finite Group Databasebeta

← Prev (#90899) Next (#90901) →

Cayley diagram

C11×C43 #90900

order473
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C22×C3×C5×C7 (order 420) · Inn(G) = C1 · Out(G) = C22×C3×C5×C7
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC473
abelianC11×C43

Subgroups

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

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 54
transitive degreeμt(G) = 473

A minimal faithful permutation representation — 1 generator on 54 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)

Conjugacy classes & character table

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

Relationships

center ofD3×C11×C43, C11×D15×C43, C11×D17×C43, …
derived subgroup ofD473, Dic473, D11×D43, …
Fitting subgroup ofD11×C43, C11×D43, D473, …
socle ofD11×C43, C11×D43, D473, …
maximal subgroup ofD11×C43, C11×D43, D473, …
maximal normal subgroup ofD11×C43, C11×D43, D473, …
maximal quotient ofC2×C11×C43, C3×C11×C43, C5×C11×C43, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(473, 1);