Finite Group Databasebeta

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C₂×C₃×C₄²×C₁₂₁ #72190054

order	11616
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 337920
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₄

Aliases

abelian	C₂×C₃×C₄²×C₁₂₁
multiplicative	(ℤ/21795)ˣ, (ℤ/23248)ˣ, (ℤ/29060)ˣ, (ℤ/43590)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₁₁	C₂³×C₃×C₁₁
socle, prime radical	C₂³×C₃×C₁₁	C₂²×C₁₁
LCS	G ▷ C₁
UCS	C₁ ◁ G

324 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11616 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₄×C₈×C₁₂₁, C₃×C₄³×C₁₂₁, C₂²×C₃×C₄²×C₁₂₁
maximal normal subgroup of	C₂×C₃×C₄×C₈×C₁₂₁, C₃×C₄³×C₁₂₁, C₂²×C₃×C₄²×C₁₂₁
maximal quotient of	C₂×C₃×C₄×C₈×C₁₂₁, C₃×C₄³×C₁₂₁, C₂²×C₃×C₄²×C₁₂₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.