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Q₃₂×D₁₆₃ #23782091

order	10432
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

Q₃₂×D₁₆₃

Splittings

Fitting	Q₃₂×C₁₆₃ ⋊ C₂
Sylow	C₁₆₃ ⋊ C₂×Q₃₂

Subgroups

	subgroup	G/H
center	C₂	D₈×D₁₆₃
commutator, cosocle	C₈×C₁₆₃	C₂³
Frattini	C₈	C₂²×D₁₆₃
Fitting	Q₃₂×C₁₆₃	C₂
socle	C₂×C₁₆₃	C₂×D₈
prime radical	C₂×D₁₆₃	D₈
hypercenter	Q₃₂	D₁₆₃
hypocenter	C₁₆₃	C₂×Q₃₂
LCS	G ▷ C₈×C₁₆₃ ▷ C₄×C₁₆₃ ▷ C₂×C₁₆₃ ▷ C₁₆₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₃₂

82 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

913 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	SD₆₄×D₁₆₃, Q₆₄×D₁₆₃, #35216852, …
maximal normal subgroup of	SD₆₄×D₁₆₃, Q₆₄×D₁₆₃, #35216852, …
maximal quotient of	#358×D₁₆₃, #366×D₁₆₃, #35216392, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10432, 975);