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D₃×D₇×C₁₀₁ #22555092

order	8484
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₀₁ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×D₇×C₁₀₁
unambiguous semidirect product	(D₃×C₇)⋊(C₂×C₁₀₁)
unambiguous semidirect product	(C₃×D₇)⋊(C₂×C₁₀₁)
unambiguous semidirect product	D₂₁⋊(C₂×C₁₀₁)

Splittings

Fitting, socle, Hall	C₃×C₇×C₁₀₁ ⋊ C₂²
derived, Hall	C₃×C₇ ⋊ C₂²×C₁₀₁
Hall	C₇×C₁₀₁ ⋊ C₂×D₃
Hall	C₃×C₁₀₁ ⋊ C₂×D₇
Sylow	C₇ ⋊ C₂×D₃×C₁₀₁
Sylow	C₃ ⋊ C₂×D₇×C₁₀₁

Subgroups

	subgroup	G/H
center, hypercenter	C₁₀₁	D₃×D₇
commutator, hypocenter	C₃×C₇	C₂²×C₁₀₁
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₀₁	C₂²
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₁₀₁

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1515 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₇×D₉×C₁₀₁, D₃×AGL(1,𝔽₇)×C₁₀₁, C₃×D₃×D₇×C₁₀₁, …
maximal normal subgroup of	D₃×AGL(1,𝔽₇)×C₁₀₁, C₃×D₃×D₇×C₁₀₁
maximal quotient of	D₇×D₉×C₁₀₁, C₃×D₃×D₇×C₁₀₁, D₃×D₂₁×C₁₀₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8484, 27);