Finite Group Databasebeta

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Dic₃×C₁₉×C₄₇ #24924263

order	10716
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₉×C₄₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	Dic₃×C₁₉×C₄₇
unambiguous semidirect product	C₃⋊(C₄×C₁₉×C₄₇)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉×C₄₇	D₃
commutator, hypocenter	C₃	C₄×C₁₉×C₄₇
Frattini	C₂	D₃×C₁₉×C₄₇
Fitting, socle, prime radical	C₂×C₃×C₁₉×C₄₇	C₂
cosocle	C₂×C₃	C₂×C₁₉×C₄₇
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₁₉×C₄₇

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5358 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₉×Dic₉×C₄₇, Dic₃×C₄₇×C₁₉⋊C₃, C₁₉×C₃⋊Dic₃×C₄₇, …
maximal normal subgroup of	Dic₃×C₄₇×C₁₉⋊C₃, C₃×Dic₃×C₁₉×C₄₇
maximal quotient of	C₁₉×Dic₉×C₄₇, C₁₉×C₃⋊Dic₃×C₄₇, C₃×Dic₃×C₁₉×C₄₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10716, 6);