C₇×C₁₁×C₁₇×C₂₅ #45658559

order	32725
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₃₂₇₂₅
abelian	C₇×C₁₁×C₁₇×C₂₅

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₅×C₇×C₁₁×C₁₇
socle, prime radical	C₅×C₇×C₁₁×C₁₇	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) = 32725

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

32725 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₃₂₇₂₅
Fitting subgroup of	D₃₂₇₂₅
maximal subgroup of	D₃₂₇₂₅
maximal normal subgroup of	D₃₂₇₂₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32725, 1);

C7×C11×C17×C25 #45658559