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C₄⋊C₈×D₁₈₁ #26041298

order	11584
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³

Aliases

C₄⋊C₈×D₁₈₁

Splittings

Fitting	C₄⋊C₈×C₁₈₁ ⋊ C₂
Sylow	C₁₈₁ ⋊ C₂×C₄⋊C₈

Subgroups

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

138 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1840 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₄⋊C₈×D₁₈₁, Q₈⋊C₈×D₁₈₁, #37532105, …
maximal normal subgroup of	D₄⋊C₈×D₁₈₁, Q₈⋊C₈×D₁₈₁, #37532105, …
maximal quotient of	#334×D₁₈₁, #335×D₁₈₁, #37532466, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11584, 568);