Finite Group Databasebeta

← Prev (#10587338) Next (#10587340) →

C11×C49 #10587339

order539
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

cyclicC539
abelianC11×C49

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC7C7×C11
socle, prime radicalC7×C11C7
LCSG ▷ C1
UCSC1 ◁ G

6 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 60
transitive degreeμt(G) = 539

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

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

Relationships

center ofD3×C11×C49, C11×D13×C49, C11×D15×C49, …
derived subgroup ofD539, Dic539, D11×D49, …
Fitting subgroup ofC11×D49, D11×C49, D539, …
maximal subgroup ofC11×D49, D11×C49, D539, …
maximal normal subgroup ofC11×D49, D11×C49, D539, …
maximal quotient ofC2×C11×C49, C3×C11×C49, C5×C11×C49, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(539, 1);