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C₂×C₃²×C₈×C₄₃ #72185376

order	6192
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 32256
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₃

Aliases

abelian	C₂×C₃²×C₈×C₄₃
multiplicative	(ℤ/7231)ˣ, (ℤ/9297)ˣ, (ℤ/14462)ˣ, (ℤ/18594)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂²×C₃²×C₄₃
socle, prime radical	C₂²×C₃²×C₄₃	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

132 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6192 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃²×C₁₆×C₄₃, C₃²×C₄×C₈×C₄₃, C₂²×C₃²×C₈×C₄₃, …
maximal normal subgroup of	C₂×C₃²×C₁₆×C₄₃, C₃²×C₄×C₈×C₄₃, C₂²×C₃²×C₈×C₄₃, …
maximal quotient of	C₂×C₃²×C₁₆×C₄₃, C₃²×C₄×C₈×C₄₃, C₂²×C₃²×C₈×C₄₃, …
automorphism group of	C₇×C₁₀₃₃, C₉×C₁₀₃₃
outer automorphism group of	C₇×C₁₀₃₃, C₉×C₁₀₃₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.