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D₇×C₁₇×D₂₁ #23756255

order	9996
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₇×C₁₇×D₂₁
unambiguous semidirect product	(C₃×D₇)⋊(D₇×C₁₇)
unambiguous semidirect product	(C₇×D₇)⋊(D₃×C₁₇)

Splittings

Fitting, socle, Hall	C₃×C₇²×C₁₇ ⋊ C₂²
derived, Hall	C₃×C₇² ⋊ C₂²×C₁₇
Hall	C₇²×C₁₇ ⋊ C₂×D₃
Hall	C₃×C₁₇ ⋊ D₇²
Sylow	C₇² ⋊ C₂×D₃×C₁₇
Sylow	C₃ ⋊ D₇²×C₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₁₇	D₇×D₂₁
commutator, cosocle, hypocenter	C₃×C₇²	C₂²×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₇	C₂²
LCS	G ▷ C₃×C₇²
UCS	C₁ ◁ C₁₇

104 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1020 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₇×C₁₇×D₆₃, C₁₇×#64418⋊D₃, D₇×C₁₇×C₃⋊AGL(1,𝔽₇), …
maximal normal subgroup of	D₇×C₁₇×C₃⋊AGL(1,𝔽₇), C₁₇×AGL(1,𝔽₇)×D₂₁, C₁₇×#64423⋊D₃, …
maximal quotient of	D₇×C₁₇×D₆₃, C₃×D₇×C₁₇×D₂₁, C₁₇×D₂₁², …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9996, 158);