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#126×D₁₈₁ #26041802

order	11584
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁴

Aliases

#126×D₁₈₁

Splittings

Fitting	#126×C₁₈₁ ⋊ C₂
Sylow	C₁₈₁ ⋊ C₂×#126

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₁₈₁
commutator, socle, cosocle	C₂²×C₁₈₁	C₂⁴
Fitting	#126×C₁₈₁	C₂
prime radical	C₂³×D₁₈₁	C₂²
hypercenter	#126	D₁₈₁
hypocenter	C₁₈₁	C₂×#126
LCS	G ▷ C₂²×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂² ◁ #126

246 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1288 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×#126×D₁₈₁, #529×D₁₈₁, #538×D₁₈₁, …
maximal normal subgroup of	C₂×#126×D₁₈₁, #529×D₁₈₁, #538×D₁₈₁, …
maximal quotient of	#383×D₁₈₁, #387×D₁₈₁, #388×D₁₈₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11584, 1072);