Finite Group Databasebeta

← Prev (#21419008) Next (#21419010) →

C₃×C₁₉×Dic₃₃ #21419009

order	7524
isoclinism	isoclinic class of D₃₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×C₁₉×Dic₃₃
unambiguous semidirect product	C₃⋊(C₃×C₁₉×Dic₁₁)
unambiguous semidirect product	C₁₁⋊(C₃×Dic₃×C₁₉)

Splittings

derived	C₃×C₁₁ ⋊ C₃×C₄×C₁₉
Hall	C₃²×C₁₁×C₁₉ ⋊ C₄
Hall	C₁₁×C₁₉ ⋊ C₃×Dic₃
Hall	C₃²×C₁₉ ⋊ Dic₁₁
Hall	C₃²×C₁₁ ⋊ C₄×C₁₉
Sylow	C₁₁ ⋊ C₃×Dic₃×C₁₉
Sylow	C₃² ⋊ C₁₉×Dic₁₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	D₃₃
commutator, hypocenter	C₃×C₁₁	C₃×C₄×C₁₉
Frattini	C₂	C₃×C₁₉×D₃₃
Fitting, socle	C₂×C₃²×C₁₁×C₁₉	C₂
LCS	G ▷ C₃×C₁₁
UCS	C₁ ◁ C₂×C₃×C₁₉

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2052 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₁₉×C₃⋊(Dic₁₁⋊C₅), C₃×C₁₉×Dic₁₆₅, C₃×C₅×C₁₉×Dic₃₃, …
maximal normal subgroup of	C₃×C₁₉×C₃⋊(Dic₁₁⋊C₅), C₃×C₅×C₁₉×Dic₃₃
maximal quotient of	C₃×C₁₉×Dic₁₆₅, C₃×C₅×C₁₉×Dic₃₃, C₃×C₁₉×C₃⋊(C₁₁⋊AGL(1,𝔽₅))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7524, 53);