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C₂×C₃×C₁₉×C₄₉ #19150246

order	5586
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₃×C₇×C₉ (order 1512) · Inn(G) = C₁ · Out(G) = C₂³×C₃×C₇×C₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₅₅₈₆
abelian	C₂×C₃×C₁₉×C₄₉

Subgroups

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

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5586 conjugacy classes. The character table is too large to display.

Relationships

center of	C₃×Dic₃×C₁₉×C₄₉, C₂×C₃×D₃×C₁₉×C₄₉
Fitting subgroup of	C₂×C₄₉×#4294, C₂×C₁₉×C₄₉⋊C₉, C₂×#22552692, …
maximal subgroup of	C₃×C₄×C₁₉×C₄₉, C₃×C₄₉×Dic₁₉, C₃×C₁₉×Dic₄₉, …
maximal normal subgroup of	C₃×C₄×C₁₉×C₄₉, C₃×C₄₉×Dic₁₉, C₃×C₁₉×Dic₄₉, …
maximal quotient of	C₃×C₄×C₁₉×C₄₉, C₂²×C₃×C₁₉×C₄₉, C₂×C₉×C₁₉×C₄₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5586, 1);