C₂²×C₃×C₅×C₁₁×C₂₉ #34062332

order	19140
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂²×C₃×C₅×C₁₁×C₂₉
multiplicative	(ℤ/19529)ˣ, (ℤ/22337)ˣ, (ℤ/28719)ˣ, (ℤ/39058)ˣ, (ℤ/44674)ˣ, (ℤ/57438)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) = 52
transitive degree	μ_t(G) = 19140

A minimal faithful permutation representation — 2 generators on 52 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);(3,4)

Conjugacy classes & character table

19140 conjugacy classes. The character table is too large to display.

Relationships

automorphism group of	C₅₉×C₃₃₁, C₇×C₃₁₉₁
outer automorphism group of	C₅₉×C₃₃₁, C₇×C₃₁₉₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19140, 25);

C22×C3×C5×C11×C29 #34062332