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C₂²×C₉×C₁₆×C₁₉ #72189485

order	10944
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 82944
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂²×C₉×C₁₆×C₁₉
multiplicative	(ℤ/18411)ˣ, (ℤ/23104)ˣ, (ℤ/24548)ˣ, (ℤ/36822)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₈	C₂³×C₃×C₁₉
socle, prime radical	C₂³×C₃×C₁₉	C₃×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

294 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10944 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₉×C₁₉×C₃₂, C₂×C₄×C₉×C₁₆×C₁₉, C₂³×C₉×C₁₆×C₁₉
maximal normal subgroup of	C₂²×C₉×C₁₉×C₃₂, C₂×C₄×C₉×C₁₆×C₁₉, C₂³×C₉×C₁₆×C₁₉
maximal quotient of	C₂²×C₉×C₁₉×C₃₂, C₂×C₄×C₉×C₁₆×C₁₉, C₂³×C₉×C₁₆×C₁₉
automorphism group of	C₆₄×C₃₆₁
outer automorphism group of	C₆₄×C₃₆₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.