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C₃²×C₁₉×Dic₁₁ #21419005

order	7524
isoclinism	isoclinic class of D₁₁
automorphism	?
homology	Abelianization (H₁) = C₃²×C₄×C₁₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃²×C₁₉×Dic₁₁
unambiguous semidirect product	C₁₁⋊(C₃²×C₄×C₁₉)

Splittings

derived, Sylow	C₁₁ ⋊ C₃²×C₄×C₁₉
Hall	C₃²×C₁₁×C₁₉ ⋊ C₄
Hall	C₁₁×C₁₉ ⋊ C₃²×C₄
Hall	C₃²×C₁₁ ⋊ C₄×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₁₉	D₁₁
commutator, hypocenter	C₁₁	C₃²×C₄×C₁₉
Frattini	C₂	C₃²×C₁₉×D₁₁
Fitting, socle	C₂×C₃²×C₁₁×C₁₉	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₃²×C₁₉

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2394 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃²×C₁₉×Dic₁₁⋊C₅, C₃²×C₁₉×Dic₅₅, C₃²×C₅×C₁₉×Dic₁₁, …
maximal normal subgroup of	C₃²×C₁₉×Dic₁₁⋊C₅, C₃²×C₅×C₁₉×Dic₁₁
maximal quotient of	C₃²×C₁₉×Dic₅₅, C₃²×C₅×C₁₉×Dic₁₁, C₃²×C₁₉×C₁₁⋊AGL(1,𝔽₅)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7524, 49);