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C₃×C₄²×C₁₂₁ #72185043

order	5808
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 21120
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄

Aliases

abelian	C₃×C₄²×C₁₂₁
multiplicative	(ℤ/7265)ˣ, (ℤ/14530)ˣ

Subgroups

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

90 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	C₃×C₄×C₈×C₁₂₁, C₂×C₃×C₄²×C₁₂₁, C₄²×C₉×C₁₂₁, …
maximal normal subgroup of	C₃×C₄×C₈×C₁₂₁, C₂×C₃×C₄²×C₁₂₁, C₄²×C₉×C₁₂₁, …
maximal quotient of	C₃×C₄×C₈×C₁₂₁, C₂×C₃×C₄²×C₁₂₁, C₄²×C₉×C₁₂₁, …
automorphism group of	C₅×C₁₄₅₃
outer automorphism group of	C₅×C₁₄₅₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.