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C2×C5×C53 #10587306

order530
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C42×C13 (order 208) · Inn(G) = C1 · Out(G) = C42×C13
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC530
abelianC2×C5×C53

Subgroups

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

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 60
transitive degreeμt(G) = 530

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

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

Relationships

center ofC5×Dic3×C53, C2×C5×D3×C53, C5×Dic13×C53, …
Fitting subgroup ofDic5×C53, C5×Dic53, Dic265, …
socle ofDic5×C53, C5×Dic53, Dic265, …
maximal subgroup ofDic5×C53, C5×Dic53, Dic265, …
maximal normal subgroup ofDic5×C53, C5×Dic53, Dic265, …
maximal quotient ofC4×C5×C53, C22×C5×C53, C5×D3×C53, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(530, 4);