C₂²×C₅×C₁₇×C₄₉ #30659377

order	16660
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂²×C₅×C₁₇×C₄₉
multiplicative	(ℤ/18337)ˣ, (ℤ/36674)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₇	C₂²×C₅×C₇×C₁₇
socle, prime radical	C₂²×C₅×C₇×C₁₇	C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 75
transitive degree	μ_t(G) = 16660

A minimal faithful permutation representation — 2 generators on 75 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);(3,4)

Conjugacy classes & character table

16660 conjugacy classes. The character table is too large to display.

Relationships

automorphism group of	C₁₁×C₁₆₆₇
outer automorphism group of	C₁₁×C₁₆₆₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16660, 9);

C22×C5×C17×C49 #30659377