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C₄×C₁₉×C₁₀₉ #22552047

order	8284
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₄×C₉×C₂₇ (order 3888) · Inn(G) = C₁ · Out(G) = C₂²×C₄×C₉×C₂₇
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₈₂₈₄
abelian	C₄×C₁₉×C₁₀₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₂	C₂×C₁₉×C₁₀₉
socle	C₂×C₁₉×C₁₀₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8284 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₈₂₈₄, D₁₆₅₆₈
Fitting subgroup of	C₄×C₁₉×C₁₀₉⋊C₃, C₄×C₁₉⋊C₃×C₁₀₉, C₄×#20261880, …
maximal subgroup of	C₃×C₄×C₁₉×C₁₀₉, C₄×C₁₉×C₁₀₉⋊C₃, C₄×C₁₉⋊C₃×C₁₀₉, …
maximal normal subgroup of	C₃×C₄×C₁₉×C₁₀₉, C₄×C₁₉×C₁₀₉⋊C₃, C₄×C₁₉⋊C₃×C₁₀₉, …
maximal quotient of	C₃×C₄×C₁₉×C₁₀₉, Dic₃×C₁₉×C₁₀₉, C₈×C₁₉×C₁₀₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8284, 1);