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C₄×C₁₉×C₁₃₉ #24902255

order	10564
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₃×C₉×C₂₃ (order 4968) · Inn(G) = C₁ · Out(G) = C₂³×C₃×C₉×C₂₃
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₅₆₄
abelian	C₄×C₁₉×C₁₃₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₁₉×C₁₃₉
socle, prime radical	C₂×C₁₉×C₁₃₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10564 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₀₅₆₄, D₂₁₁₂₈
Fitting subgroup of	C₄×C₁₉×C₁₃₉⋊C₃, C₄×C₁₉⋊C₃×C₁₃₉, C₄×#21463701, …
maximal subgroup of	C₃×C₄×C₁₉×C₁₃₉, C₄×C₁₉×C₁₃₉⋊C₃, C₄×C₁₉⋊C₃×C₁₃₉, …
maximal normal subgroup of	C₃×C₄×C₁₉×C₁₃₉, C₄×C₁₉×C₁₃₉⋊C₃, C₄×C₁₉⋊C₃×C₁₃₉, …
maximal quotient of	C₃×C₄×C₁₉×C₁₃₉, Dic₃×C₁₉×C₁₃₉, C₈×C₁₉×C₁₃₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10564, 1);