Finite Group Databasebeta

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D₃×C₁₉×C₆₇ #21439399

order	7638
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₉×C₆₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃×C₁₉×C₆₇
unambiguous semidirect product	C₃⋊(C₂×C₁₉×C₆₇)

Splittings

Fitting, socle, Hall	C₃×C₁₉×C₆₇ ⋊ C₂
derived, Sylow	C₃ ⋊ C₂×C₁₉×C₆₇
Hall	C₃×C₆₇ ⋊ C₂×C₁₉
Hall	C₃×C₁₉ ⋊ C₂×C₆₇

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉×C₆₇	D₃
commutator, hypocenter	C₃	C₂×C₁₉×C₆₇
Frattini	C₁	G
Fitting, socle	C₃×C₁₉×C₆₇	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₁₉×C₆₇

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3819 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₃×C₁₉×D₆₇, D₃×D₁₉×C₆₇, D₃×D₁₂₇₃, …
maximal normal subgroup of	D₃×C₁₉×D₆₇, D₃×D₁₉×C₆₇, D₃×D₁₂₇₃, …
maximal quotient of	Dic₃×C₁₉×C₆₇, C₂×D₃×C₁₉×C₆₇, D₉×C₁₉×C₆₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7638, 9);