C₂×C₃×C₁₁×C₁₇×C₁₉ #36319256

order	21318
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₂₁₃₁₈
abelian	C₂×C₃×C₁₁×C₁₇×C₁₉
multiplicative	(ℤ/21319)ˣ, (ℤ/42638)ˣ

Subgroups

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

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 52
transitive degree	μ_t(G) = 21318

A minimal faithful permutation representation — 1 generator on 52 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)

Conjugacy classes & character table

21318 conjugacy classes. The character table is too large to display.

Relationships

automorphism group of	C₂₁₃₁₉
outer automorphism group of	C₂₁₃₁₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21318, 1);

C2×C3×C11×C17×C19 #36319256