C₅²×C₉×C₅₉ #27210757

order	13275
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₅

Aliases

abelian

C₅²×C₉×C₅₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₃×C₅²×C₅₉
socle, prime radical	C₃×C₅²×C₅₉	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 78
transitive degree	μ_t(G) = 13275

A minimal faithful permutation representation — 2 generators on 78 points:

(1,2,3,4,5,6,7,8,9)(10,11,12,13,14)(20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78);(15,16,17,18,19)

Conjugacy classes & character table

13275 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	C₅⋊D₂₆₅₅
Fitting subgroup of	C₅²×C₉×D₅₉, C₅×C₉×D₅×C₅₉, C₅×C₉×D₂₉₅, …
maximal subgroup of	C₂×C₅²×C₉×C₅₉, C₅²×C₉×D₅₉, C₅×C₉×D₅×C₅₉, …
maximal normal subgroup of	C₂×C₅²×C₉×C₅₉, C₅²×C₉×D₅₉, C₅×C₉×D₅×C₅₉, …
maximal quotient of	C₂×C₅²×C₉×C₅₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13275, 3);

C52×C9×C59 #27210757