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D₃×D₇×C₁₆₉ #28382129

order	14196
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₆₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×D₇×C₁₆₉
unambiguous semidirect product	(D₃×C₇)⋊(C₂×C₁₆₉)
unambiguous semidirect product	(C₃×D₇)⋊(C₂×C₁₆₉)
unambiguous semidirect product	D₂₁⋊(C₂×C₁₆₉)

Splittings

Fitting, Hall	C₃×C₇×C₁₆₉ ⋊ C₂²
derived, Hall	C₃×C₇ ⋊ C₂²×C₁₆₉
Hall	C₇×C₁₆₉ ⋊ C₂×D₃
Hall	C₃×C₁₆₉ ⋊ C₂×D₇
Sylow	C₇ ⋊ C₂×D₃×C₁₆₉
Sylow	C₃ ⋊ C₂×D₇×C₁₆₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₆₉	D₃×D₇
commutator, hypocenter	C₃×C₇	C₂²×C₁₆₉
Frattini	C₁₃	D₃×C₁₃×D₇
Fitting	C₃×C₇×C₁₆₉	C₂²
socle, cosocle	C₃×C₇×C₁₃	C₂²×C₁₃
prime radical	D₃×C₁₃×D₇	C₁₃
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₁₆₉

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2535 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14196, 57);