C₃×C₁₃×C₁₉×C₂₅ #32915087

order	18525
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₈₅₂₅
abelian	C₃×C₁₃×C₁₉×C₂₅

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₃×C₅×C₁₃×C₁₉
socle, prime radical	C₃×C₅×C₁₃×C₁₉	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 60
transitive degree	μ_t(G) = 18525

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

18525 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₁₈₅₂₅
Fitting subgroup of	C₃×C₁₃×C₂₅×D₁₉, C₃×C₁₉×C₂₅×D₁₃, C₃×C₂₅×D₂₄₇, …
maximal subgroup of	C₂×C₃×C₁₃×C₁₉×C₂₅, C₃×C₁₃×C₂₅×D₁₉, C₃×C₁₉×C₂₅×D₁₃, …
maximal normal subgroup of	C₂×C₃×C₁₃×C₁₉×C₂₅, C₃×C₁₃×C₂₅×D₁₉, C₃×C₁₉×C₂₅×D₁₃, …
maximal quotient of	C₂×C₃×C₁₃×C₁₉×C₂₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18525, 1);

C3×C13×C19×C25 #32915087