Finite Group Databasebeta

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C₁₁×C₁₉×Dic₁₃ #24925870

order	10868
isoclinism	isoclinic class of D₁₃
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₁×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₁₁×C₁₉×Dic₁₃

Splittings

derived, Sylow	C₁₃ ⋊ C₄×C₁₁×C₁₉
Hall	C₁₁×C₁₃×C₁₉ ⋊ C₄
Hall	C₁₃×C₁₉ ⋊ C₄×C₁₁
Hall	C₁₁×C₁₃ ⋊ C₄×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₁×C₁₉	D₁₃
commutator, hypocenter	C₁₃	C₄×C₁₁×C₁₉
Frattini	C₂	C₁₁×C₁₉×D₁₃
Fitting, socle, prime radical	C₂×C₁₁×C₁₃×C₁₉	C₂
cosocle	C₂×C₁₃	C₂×C₁₁×C₁₉
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₁₁×C₁₉

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3344 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₁₁×C₁₉×Dic₁₃, C₁₁×C₁₉×Dic₃₉, C₁₁×Dic₁₃×C₁₉⋊C₃, …
maximal normal subgroup of	C₃×C₁₁×C₁₉×Dic₁₃, C₁₁×Dic₁₃×C₁₉⋊C₃, C₁₁×C₁₉×Dic₁₃⋊C₃, …
maximal quotient of	C₃×C₁₁×C₁₉×Dic₁₃, C₁₁×C₁₉×Dic₃₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10868, 3);