C₃×C₁₆×C₄₁ #14520081

order	1968
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₄×C₅×C₈ (order 640) · Inn(G) = C₁ · Out(G) = C₂²×C₄×C₅×C₈
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₉₆₈
abelian	C₃×C₁₆×C₄₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₃×C₄₁
socle, prime radical	C₂×C₃×C₄₁	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 60
transitive degree	μ_t(G) = 1968

A minimal faithful permutation representation — 1 generator on 60 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)(17,18,19)(20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60)

Conjugacy classes & character table

1968 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₃₂×C₄₁, C₂×C₃×C₁₆×C₄₁, C₉×C₁₆×C₄₁, …
maximal normal subgroup of	C₃×C₃₂×C₄₁, C₂×C₃×C₁₆×C₄₁, C₉×C₁₆×C₄₁, …
maximal quotient of	C₃×C₃₂×C₄₁, C₂×C₃×C₁₆×C₄₁, C₉×C₁₆×C₄₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1968, 4);

C3×C16×C41 #14520081