C₂²×C₃×C₅×C₇×C₆₁ #38785000

order	25620
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂²×C₃×C₅×C₇×C₆₁
multiplicative	(ℤ/26057)ˣ, (ℤ/29897)ˣ, (ℤ/38439)ˣ, (ℤ/52114)ˣ, (ℤ/59794)ˣ, (ℤ/76878)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) = 80
transitive degree	μ_t(G) = 25620

A minimal faithful permutation representation — 2 generators on 80 points:

(1,2)(5,6,7)(8,9,10,11,12)(13,14,15,16,17,18,19)(20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80);(3,4)

Conjugacy classes & character table

25620 conjugacy classes. The character table is too large to display.

Relationships

automorphism group of	C₇₁×C₃₆₇
outer automorphism group of	C₇₁×C₃₆₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25620, 73);

C22×C3×C5×C7×C61 #38785000