C₂×C₅×C₇×C₉×C₃₁ #34086096

order	19530
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₉₅₃₀
abelian	C₂×C₅×C₇×C₉×C₃₁
multiplicative	(ℤ/19531)ˣ, (ℤ/39062)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂×C₃×C₅×C₇×C₃₁
socle, prime radical	C₂×C₃×C₅×C₇×C₃₁	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 54
transitive degree	μ_t(G) = 19530

A minimal faithful permutation representation — 1 generator on 54 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)

Conjugacy classes & character table

19530 conjugacy classes. The character table is too large to display.

Relationships

automorphism group of	C₁₉₅₃₁
outer automorphism group of	C₁₉₅₃₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 1);

C2×C5×C7×C9×C31 #34086096