C₃²×C₂₅×C₅₉ #27210756

order	13275
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃

Aliases

abelian

C₃²×C₂₅×C₅₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₃²×C₅×C₅₉
socle, prime radical	C₃²×C₅×C₅₉	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 90
transitive degree	μ_t(G) = 13275

A minimal faithful permutation representation — 2 generators on 90 points:

(1,2,3)(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)(32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90);(4,5,6)

Conjugacy classes & character table

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

Relationships

derived subgroup of	C₃⋊D₄₄₂₅
Fitting subgroup of	C₃²×C₂₅×D₅₉, C₃²×D₂₅×C₅₉, C₃²×D₁₄₇₅, …
maximal subgroup of	C₂×C₃²×C₂₅×C₅₉, C₃²×C₂₅×D₅₉, C₃²×D₂₅×C₅₉, …
maximal normal subgroup of	C₂×C₃²×C₂₅×C₅₉, C₃²×C₂₅×D₅₉, C₃²×D₂₅×C₅₉, …
maximal quotient of	C₂×C₃²×C₂₅×C₅₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13275, 2);

C32×C25×C59 #27210756