Finite Group Databasebeta

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C₃×C₁₉×Dic₅₃ #27130571

order	12084
isoclinism	isoclinic class of D₅₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₃×C₁₉×Dic₅₃

Splittings

derived, Sylow	C₅₃ ⋊ C₃×C₄×C₁₉
Hall	C₃×C₁₉×C₅₃ ⋊ C₄
Hall	C₁₉×C₅₃ ⋊ C₃×C₄
Hall	C₃×C₅₃ ⋊ C₄×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	D₅₃
commutator, hypocenter	C₅₃	C₃×C₄×C₁₉
Frattini	C₂	C₃×C₁₉×D₅₃
Fitting, socle, prime radical	C₂×C₃×C₁₉×C₅₃	C₂
cosocle	C₂×C₅₃	C₂×C₃×C₁₉
LCS	G ▷ C₅₃
UCS	C₁ ◁ C₂×C₃×C₁₉

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3192 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×C₁₉×Dic₅₃, #4294×Dic₅₃, C₃×C₁₉⋊C₃×Dic₅₃, …
maximal normal subgroup of	C₉×C₁₉×Dic₅₃, #4294×Dic₅₃, C₃×C₁₉⋊C₃×Dic₅₃, …
maximal quotient of	C₉×C₁₉×Dic₅₃, C₃×C₁₉×Dic₁₅₉, C₃²×C₁₉×Dic₅₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12084, 3);