Finite Group Databasebeta

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D₃×D₁₆₁ #14515387

order	1932
isoclinism	isoclinic class of D₃×D₁₆₁
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×D₁₆₁
unambiguous semidirect product	(D₃×C₇)⋊D₂₃
unambiguous semidirect product	(D₃×C₂₃)⋊D₇

Splittings

Fitting, socle, derived, Hall	C₃×C₇×C₂₃ ⋊ C₂²
Hall	C₇×C₂₃ ⋊ C₂×D₃
Hall	C₃×C₂₃ ⋊ C₂×D₇
Sylow	C₂₃ ⋊ D₃×D₇
Hall	C₃×C₇ ⋊ C₂×D₂₃
Sylow	C₇ ⋊ D₃×D₂₃
Sylow	C₃ ⋊ C₂×D₁₆₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₂₃	C₂²
LCS	G ▷ C₃×C₇×C₂₃
UCS	C₁

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 483

Conjugacy classes & character table

246 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×D₁₁₂₇, D₃×C₇×D₁₆₁, D₃×C₇⋊D₁₆₁, …
maximal normal subgroup of	D₃×C₇×D₁₆₁, D₃×C₇⋊AGL(1,𝔽₂₃), D₃×C₁₁×D₁₆₁, …
maximal quotient of	D₃×D₁₁₂₇, D₃×C₇×D₁₆₁, D₃×C₇⋊D₁₆₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1932, 22);