Finite Group Databasebeta

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C₂×C₄²×D₁₈₁ #26041723

order	11584
isoclinism	isoclinic class of D₁₈₁
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

C₂×C₄²×D₁₈₁

Splittings

Fitting	C₂×C₄²×C₁₈₁ ⋊ C₂
derived, Sylow	C₁₈₁ ⋊ C₂²×C₄²

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₄²	D₁₈₁
commutator, hypocenter	C₁₈₁	C₂²×C₄²
Frattini	C₂²	C₂³×D₁₈₁
Fitting	C₂×C₄²×C₁₈₁	C₂
socle	C₂³×C₁₈₁	C₂³
prime radical	C₂³×D₁₈₁	C₂²
cosocle	C₂²×C₁₈₁	C₂⁴
LCS	G ▷ C₁₈₁
UCS	C₁ ◁ C₂×C₄²

498 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2944 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	#336×D₁₈₁, #37533413, #339×D₁₈₁, …
maximal normal subgroup of	#336×D₁₈₁, #37533413, #339×D₁₈₁, …
maximal quotient of	C₄³×D₁₈₁, C₂×C₄²×Dic₁₈₁, C₂×#95×D₁₈₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11584, 993);