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C₂²×C₃³×C₈×C₁₃ #72189718

order	11232
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 51757056
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₃³

Aliases

abelian	C₂²×C₃³×C₈×C₁₃
multiplicative	(ℤ/19719)ˣ, (ℤ/39438)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂³×C₃³×C₁₃
socle, prime radical	C₂³×C₃³×C₁₃	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

2128 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11232 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₃³×C₁₃×C₁₆, C₂×C₃³×C₄×C₈×C₁₃, C₂³×C₃³×C₈×C₁₃
maximal normal subgroup of	C₂²×C₃³×C₁₃×C₁₆, C₂×C₃³×C₄×C₈×C₁₃, C₂³×C₃³×C₈×C₁₃
maximal quotient of	C₂²×C₃³×C₁₃×C₁₆, C₂×C₃³×C₄×C₈×C₁₃, C₂³×C₃³×C₈×C₁₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.