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C₂²×C₃×C₄×C₁₂₁ #72185045

order	5808
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 42240
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂²×C₃×C₄×C₁₂₁
multiplicative	(ℤ/10905)ˣ, (ℤ/11624)ˣ, (ℤ/11632)ˣ, (ℤ/14540)ˣ, (ℤ/17436)ˣ, (ℤ/21810)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₁₁	C₂³×C₃×C₁₁
socle, prime radical	C₂³×C₃×C₁₁	C₂×C₁₁
LCS	G ▷ C₁
UCS	C₁ ◁ G

162 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5808 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₃×C₈×C₁₂₁, C₂×C₃×C₄²×C₁₂₁, C₂³×C₃×C₄×C₁₂₁, …
maximal normal subgroup of	C₂²×C₃×C₈×C₁₂₁, C₂×C₃×C₄²×C₁₂₁, C₂³×C₃×C₄×C₁₂₁, …
maximal quotient of	C₂²×C₃×C₈×C₁₂₁, C₂×C₃×C₄²×C₁₂₁, C₂³×C₃×C₄×C₁₂₁, …
automorphism group of	C₃×C₅×C₇₂₇
outer automorphism group of	C₃×C₅×C₇₂₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.