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C₄×C₄₇×C₁₉⋊C₃ #24924259

order	10716
isoclinism	isoclinic class of C₁₉⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₄₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₄×C₄₇×C₁₉⋊C₃
unambiguous semidirect product	(C₄×C₁₉)⋊(C₃×C₄₇)
unambiguous semidirect product	(C₄×C₁₉×C₄₇)⋊C₃

Splittings

Fitting, Hall	C₄×C₁₉×C₄₇ ⋊ C₃
derived, Sylow	C₁₉ ⋊ C₃×C₄×C₄₇
Hall	C₁₉×C₄₇ ⋊ C₃×C₄
Hall	C₄×C₁₉ ⋊ C₃×C₄₇

Subgroups

	subgroup	G/H
center, hypercenter	C₄×C₄₇	C₁₉⋊C₃
commutator, hypocenter	C₁₉	C₃×C₄×C₄₇
Frattini	C₂	C₂×C₄₇×C₁₉⋊C₃
Fitting	C₄×C₁₉×C₄₇	C₃
socle	C₂×C₁₉×C₄₇	C₂×C₃
prime radical	C₂×C₄₇×C₁₉⋊C₃	C₂
cosocle	C₂×C₁₉	C₂×C₃×C₄₇
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₄×C₄₇

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1692 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₄₇×#4296, Dic₃×C₄₇×C₁₉⋊C₃, C₃×C₄×C₄₇×C₁₉⋊C₃
maximal normal subgroup of	C₄×C₄₇×#4296, C₃×C₄×C₄₇×C₁₉⋊C₃
maximal quotient of	C₄×C₄₇×#4294, Dic₃×C₄₇×C₁₉⋊C₃, C₃×C₄×C₄₇×C₁₉⋊C₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10716, 2);