C₂²×C₃×C₅×C₇×C₄₃ #31825385

order	18060
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂²×C₃×C₅×C₇×C₄₃
multiplicative	(ℤ/18533)ˣ, (ℤ/20339)ˣ, (ℤ/21077)ˣ, (ℤ/21119)ˣ, (ℤ/27099)ˣ, (ℤ/37066)ˣ, (ℤ/40678)ˣ, (ℤ/42154)ˣ, (ℤ/42238)ˣ, (ℤ/54198)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 62
transitive degree	μ_t(G) = 18060

A minimal faithful permutation representation — 2 generators on 62 points:

(1,2)(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);(3,4)

Conjugacy classes & character table

18060 conjugacy classes. The character table is too large to display.

Relationships

automorphism group of	C₄₃×C₄₃₁, C₇×C₃₀₁₁
outer automorphism group of	C₄₃×C₄₃₁, C₇×C₃₀₁₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18060, 61);

C22×C3×C5×C7×C43 #31825385