C₅²×C₁₃×C₄₉ #30629935

order	15925
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₅

Aliases

abelian

C₅²×C₁₃×C₄₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₇	C₅²×C₇×C₁₃
socle, prime radical	C₅²×C₇×C₁₃	C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 72
transitive degree	μ_t(G) = 15925

A minimal faithful permutation representation — 2 generators on 72 points:

(1,2,3,4,5)(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);(6,7,8,9,10)

Conjugacy classes & character table

15925 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	C₅⋊D₃₁₈₅
Fitting subgroup of	C₅²×D₁₃×C₄₉, C₅²×C₁₃×D₄₉, C₅²×D₆₃₇, …
maximal subgroup of	C₂×C₅²×C₁₃×C₄₉, C₅²×D₁₃×C₄₉, C₅²×C₁₃×D₄₉, …
maximal normal subgroup of	C₂×C₅²×C₁₃×C₄₉, C₅²×D₁₃×C₄₉, C₅²×C₁₃×D₄₉, …
maximal quotient of	C₂×C₅²×C₁₃×C₄₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15925, 2);

C52×C13×C49 #30629935