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C₄×C₁₉×C₇₉ #20238762

order	6004
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₃×C₉×C₁₃ (order 2808) · Inn(G) = C₁ · Out(G) = C₂³×C₃×C₉×C₁₃
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₆₀₀₄
abelian	C₄×C₁₉×C₇₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₂	C₂×C₁₉×C₇₉
socle	C₂×C₁₉×C₇₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6004 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₄×C₁₉×C₇₉⋊C₃, C₄×C₁₉⋊C₃×C₇₉, C₄×#17985163, …
maximal subgroup of	C₃×C₄×C₁₉×C₇₉, C₄×C₁₉×C₇₉⋊C₃, C₄×C₁₉⋊C₃×C₇₉, …
maximal normal subgroup of	C₃×C₄×C₁₉×C₇₉, C₄×C₁₉×C₇₉⋊C₃, C₄×C₁₉⋊C₃×C₇₉, …
maximal quotient of	C₃×C₄×C₁₉×C₇₉, Dic₃×C₁₉×C₇₉, C₄×C₅×C₁₉×C₇₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6004, 1);