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D₃×D₇×C₁₀₃ #22575772

order	8652
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₀₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×D₇×C₁₀₃
unambiguous semidirect product	(D₃×C₇)⋊(C₂×C₁₀₃)
unambiguous semidirect product	(C₃×D₇)⋊(C₂×C₁₀₃)
unambiguous semidirect product	D₂₁⋊(C₂×C₁₀₃)

Splittings

Fitting, socle, Hall	C₃×C₇×C₁₀₃ ⋊ C₂²
derived, Hall	C₃×C₇ ⋊ C₂²×C₁₀₃
Hall	C₇×C₁₀₃ ⋊ C₂×D₃
Hall	C₃×C₁₀₃ ⋊ C₂×D₇
Sylow	C₇ ⋊ C₂×D₃×C₁₀₃
Sylow	C₃ ⋊ C₂×D₇×C₁₀₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₀₃	D₃×D₇
commutator, hypocenter	C₃×C₇	C₂²×C₁₀₃
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₀₃	C₂²
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₁₀₃

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1545 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₇×D₉×C₁₀₃, D₃×AGL(1,𝔽₇)×C₁₀₃, D₃×#16864502, …
maximal normal subgroup of	D₃×AGL(1,𝔽₇)×C₁₀₃, D₃×#16864502, D₃×#16864501, …
maximal quotient of	D₇×D₉×C₁₀₃, C₃×D₃×D₇×C₁₀₃, D₃×D₂₁×C₁₀₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8652, 45);