C₇×C₉×C₁₁×C₂₅ #31773141

order	17325
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₇₃₂₅
abelian	C₇×C₉×C₁₁×C₂₅

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₅	C₃×C₅×C₇×C₁₁
socle, prime radical	C₃×C₅×C₇×C₁₁	C₃×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 52
transitive degree	μ_t(G) = 17325

A minimal faithful permutation representation — 1 generator on 52 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)

Conjugacy classes & character table

17325 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₁₇₃₂₅
Fitting subgroup of	C₇×C₉×D₁₁×C₂₅, C₉×C₁₁×D₇×C₂₅, C₉×C₂₅×D₇₇, …
maximal subgroup of	C₂×C₇×C₉×C₁₁×C₂₅, C₇×C₉×D₁₁×C₂₅, C₉×C₁₁×D₇×C₂₅, …
maximal normal subgroup of	C₂×C₇×C₉×C₁₁×C₂₅, C₇×C₉×D₁₁×C₂₅, C₉×C₁₁×D₇×C₂₅, …
maximal quotient of	C₂×C₇×C₉×C₁₁×C₂₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17325, 1);

C7×C9×C11×C25 #31773141