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C₄×C₁₁×C₁₃×C₁₉ #24925868

order	10868
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₃×C₄×C₅×C₉ (order 4320) · Inn(G) = C₁ · Out(G) = C₂³×C₃×C₄×C₅×C₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₈₆₈
abelian	C₄×C₁₁×C₁₃×C₁₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₁₁×C₁₃×C₁₉
socle, prime radical	C₂×C₁₁×C₁₃×C₁₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10868 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₀₈₆₈, D₂₁₇₃₆
Fitting subgroup of	C₄×C₁₁×C₁₃×C₁₉⋊C₃, C₄×C₁₁×C₁₉×C₁₃⋊C₃, C₄×C₁₁×#10625202, …
maximal subgroup of	C₃×C₄×C₁₁×C₁₃×C₁₉, C₄×C₁₁×C₁₃×C₁₉⋊C₃, C₄×C₁₁×C₁₉×C₁₃⋊C₃, …
maximal normal subgroup of	C₃×C₄×C₁₁×C₁₃×C₁₉, C₄×C₁₁×C₁₃×C₁₉⋊C₃, C₄×C₁₁×C₁₉×C₁₃⋊C₃, …
maximal quotient of	C₃×C₄×C₁₁×C₁₃×C₁₉, C₁₁×Dic₃×C₁₃×C₁₉, C₈×C₁₁×C₁₃×C₁₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10868, 1);