C₂×C₉×C₁₉×C₄₉ #30660474

order	16758
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₆₇₅₈
abelian	C₂×C₉×C₁₉×C₄₉
multiplicative	(ℤ/16759)ˣ, (ℤ/33518)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₇	C₂×C₃×C₇×C₁₉
socle, prime radical	C₂×C₃×C₇×C₁₉	C₃×C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 79
transitive degree	μ_t(G) = 16758

A minimal faithful permutation representation — 1 generator on 79 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)(61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79)

Conjugacy classes & character table

16758 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₉×C₄₉×Dic₁₉, C₉×C₁₉×Dic₄₉, C₉×Dic₉₃₁, …
maximal subgroup of	C₄×C₉×C₁₉×C₄₉, C₉×C₄₉×Dic₁₉, C₉×C₁₉×Dic₄₉, …
maximal normal subgroup of	C₄×C₉×C₁₉×C₄₉, C₉×C₄₉×Dic₁₉, C₉×C₁₉×Dic₄₉, …
maximal quotient of	C₄×C₉×C₁₉×C₄₉, C₂²×C₉×C₁₉×C₄₉
automorphism group of	C₁₆₇₅₉
outer automorphism group of	C₁₆₇₅₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16758, 1);

C2×C9×C19×C49 #30660474