C₄×C₅×C₉×C₁₀₁ #32911368

order	18180
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₈₁₈₀
abelian	C₄×C₅×C₉×C₁₀₁
multiplicative	(ℤ/18181)ˣ, (ℤ/36362)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂×C₃×C₅×C₁₀₁
socle, prime radical	C₂×C₃×C₅×C₁₀₁	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 119
transitive degree	μ_t(G) = 18180

A minimal faithful permutation representation — 1 generator on 119 points:

(1,2,3,4)(5,6,7,8,9,10,11,12,13)(14,15,16,17,18)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119)

Conjugacy classes & character table

18180 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₉₀₉₀, D₁₈₁₈₀
maximal subgroup of	Dic₉₀₉₀, D₁₈₁₈₀
maximal normal subgroup of	Dic₉₀₉₀, D₁₈₁₈₀
automorphism group of	C₁₈₁₈₁
outer automorphism group of	C₁₈₁₈₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18180, 1);

C4×C5×C9×C101 #32911368