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Q₃₂×D₁₈₁ #26041705

order	11584
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

Q₃₂×D₁₈₁

Splittings

Fitting	Q₃₂×C₁₈₁ ⋊ C₂
Sylow	C₁₈₁ ⋊ C₂×Q₃₂

Subgroups

	subgroup	G/H
center	C₂	D₈×D₁₈₁
commutator, cosocle	C₈×C₁₈₁	C₂³
Frattini	C₈	C₂²×D₁₈₁
Fitting	Q₃₂×C₁₈₁	C₂
socle	C₂×C₁₈₁	C₂×D₈
prime radical	C₂×D₁₈₁	D₈
hypercenter	Q₃₂	D₁₈₁
hypocenter	C₁₈₁	C₂×Q₃₂
LCS	G ▷ C₈×C₁₈₁ ▷ C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₃₂

82 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	SD₆₄×D₁₈₁, Q₆₄×D₁₈₁, #37536037, …
maximal normal subgroup of	SD₆₄×D₁₈₁, Q₆₄×D₁₈₁, #37536037, …
maximal quotient of	#358×D₁₈₁, #366×D₁₈₁, #37535577, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11584, 975);