C₅×C₈×C₄₉ #14519907

order	1960
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₃×C₄×C₇ (order 672) · Inn(G) = C₁ · Out(G) = C₂³×C₃×C₄×C₇
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₉₆₀
abelian	C₅×C₈×C₄₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₇	C₂×C₅×C₇
socle, prime radical	C₂×C₅×C₇	C₄×C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 62
transitive degree	μ_t(G) = 1960

A minimal faithful permutation representation — 1 generator on 62 points:

(1,2,3,4,5,6,7,8)(9,10,11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62)

Conjugacy classes & character table

1960 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×C₁₆×C₄₉, C₂×C₅×C₈×C₄₉, C₃×C₅×C₈×C₄₉, …
maximal normal subgroup of	C₅×C₁₆×C₄₉, C₂×C₅×C₈×C₄₉, C₃×C₅×C₈×C₄₉, …
maximal quotient of	C₅×C₁₆×C₄₉, C₂×C₅×C₈×C₄₉, C₃×C₅×C₈×C₄₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1960, 4);

C5×C8×C49 #14519907