C₅×C₉×C₁₃×C₅₃ #44526513

order	31005
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₃₁₀₀₅
abelian	C₅×C₉×C₁₃×C₅₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₃×C₅×C₁₃×C₅₃
socle, prime radical	C₃×C₅×C₁₃×C₅₃	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 80
transitive degree	μ_t(G) = 31005

A minimal faithful permutation representation — 1 generator on 80 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)(28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80)

Conjugacy classes & character table

31005 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₃₁₀₀₅
Fitting subgroup of	D₃₁₀₀₅
maximal subgroup of	D₃₁₀₀₅
maximal normal subgroup of	D₃₁₀₀₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31005, 1);

C5×C9×C13×C53 #44526513