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C₂×C₄×Q₈×C₁₈₁ #26040927

order	11584
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₈₁ · Schur multiplier (H₂) = C₂⁵

Aliases

C₂×C₄×Q₈×C₁₈₁

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₈₁	C₂²
commutator	C₂	C₂³×C₄×C₁₈₁
Frattini, cosocle	C₂²	C₂⁴×C₁₈₁
socle, prime radical	C₂³×C₁₈₁	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₈₁ ◁ G

298 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7240 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#37532045, #37532065, C₂×Q₈⋊#13089678, …
maximal subgroup of	#1461×C₁₈₁, #1467×C₁₈₁, C₂×Q₈⋊C₈×C₁₈₁, …
maximal normal subgroup of	#1461×C₁₈₁, #1467×C₁₈₁, C₂×Q₈⋊C₈×C₁₈₁, …
maximal quotient of	C₂×C₄×C₄⋊C₄×C₁₈₁, C₄²×Q₈×C₁₈₁, C₂×#387×C₁₈₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11584, 197);