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C₂²×C₃×C₉×C₇₁ #72186583

order	7668
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 45360
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₃

Aliases

abelian	C₂²×C₃×C₉×C₇₁
multiplicative	(ℤ/8953)ˣ, (ℤ/11511)ˣ, (ℤ/17906)ˣ, (ℤ/23022)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂²×C₃²×C₇₁
socle, prime radical	C₂²×C₃²×C₇₁	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

100 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7668 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₄×C₉×C₇₁, C₂³×C₃×C₉×C₇₁, C₂²×C₃×C₂₇×C₇₁, …
maximal normal subgroup of	C₂×C₃×C₄×C₉×C₇₁, C₂³×C₃×C₉×C₇₁, C₂²×C₃×C₂₇×C₇₁, …
maximal quotient of	C₂×C₃×C₄×C₉×C₇₁, C₂³×C₃×C₉×C₇₁, C₂²×C₃×C₂₇×C₇₁, …
automorphism group of	C₇×C₁₂₇₉
outer automorphism group of	C₇×C₁₂₇₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.