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C₂³×C₉×C₁₃₁ #72188199

order	9432
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 131040
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂³×C₉×C₁₃₁
multiplicative	(ℤ/14991)ˣ, (ℤ/19988)ˣ, (ℤ/28404)ˣ, (ℤ/29982)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂³×C₃×C₁₃₁
socle, prime radical	C₂³×C₃×C₁₃₁	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9432 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₄×C₉×C₁₃₁, C₂⁴×C₉×C₁₃₁, C₂³×C₂₇×C₁₃₁, …
maximal normal subgroup of	C₂²×C₄×C₉×C₁₃₁, C₂⁴×C₉×C₁₃₁, C₂³×C₂₇×C₁₃₁, …
maximal quotient of	C₂²×C₄×C₉×C₁₃₁, C₂⁴×C₉×C₁₃₁, C₂³×C₂₇×C₁₃₁, …
automorphism group of	C₄×C₂₇×C₂₆₃
outer automorphism group of	C₄×C₂₇×C₂₆₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.