Finite Group Databasebeta

← Prev (#10620238) Next (#10620240) →

C11×C59 #10620239

order649
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C22×C5×C29 (order 580) · Inn(G) = C1 · Out(G) = C22×C5×C29
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC649
abelianC11×C59

Subgroups

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

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 70
transitive degreeμt(G) = 649

A minimal faithful permutation representation — 1 generator on 70 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)

Conjugacy classes & character table

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

Relationships

center ofD3×C11×C59, C11×ΓL(1,𝔽8)×C59, C11×D11×C59, …
derived subgroup ofD649, Dic649, D11×D59, …
Fitting subgroup ofD11×C59, C11×D59, D649, …
socle ofD11×C59, C11×D59, D649, …
maximal subgroup ofD11×C59, C11×D59, D649, …
maximal normal subgroup ofD11×C59, C11×D59, D649, …
maximal quotient ofC2×C11×C59, C3×C11×C59, C5×C11×C59, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(649, 1);