Finite Group Databasebeta

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C₃×C₄₇×C₁₉⋊C₃ #22548829

order	8037
isoclinism	isoclinic class of C₁₉⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃²×C₄₇ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×C₄₇×C₁₉⋊C₃
unambiguous semidirect product	C₁₉⋊(C₃²×C₄₇)
unambiguous semidirect product	(C₃×C₁₉)⋊(C₃×C₄₇)
unambiguous semidirect product	(C₁₉×C₄₇)⋊C₃²
unambiguous semidirect product	(C₃×C₁₉×C₄₇)⋊C₃

Splittings

Fitting, socle	C₃×C₁₉×C₄₇ ⋊ C₃
derived, Sylow	C₁₉ ⋊ C₃²×C₄₇
Hall	C₁₉×C₄₇ ⋊ C₃²

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₄₇	C₁₉⋊C₃
commutator, hypocenter	C₁₉	C₃²×C₄₇
Frattini	C₁	G
Fitting, socle	C₃×C₁₉×C₄₇	C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₃×C₄₇

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1269 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₄₇×D₁₉⋊C₃, C₃×C₄₇⋊(D₁₉⋊C₃), C₃×C₁₉⋊C₃×D₄₇, …
maximal normal subgroup of	C₃×C₄₇×D₁₉⋊C₃, C₃×C₄₇⋊(D₁₉⋊C₃), C₃×C₁₉⋊C₃×D₄₇, …
maximal quotient of	C₂×C₃×C₄₇×C₁₉⋊C₃, A₄×C₄₇×C₁₉⋊C₃, C₃×C₄₇×C₂²⋊(C₁₉⋊C₃)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8037, 5);