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C₂²×C₄×C₉×C₄₃ #72185379

order	6192
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 48384
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂²×C₄×C₉×C₄₃
multiplicative	(ℤ/9861)ˣ, (ℤ/12392)ˣ, (ℤ/13148)ˣ, (ℤ/18588)ˣ, (ℤ/18684)ˣ, (ℤ/19722)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂³×C₃×C₄₃
socle, prime radical	C₂³×C₃×C₄₃	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

162 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	C₂²×C₈×C₉×C₄₃, C₂×C₄²×C₉×C₄₃, C₂³×C₄×C₉×C₄₃, …
maximal normal subgroup of	C₂²×C₈×C₉×C₄₃, C₂×C₄²×C₉×C₄₃, C₂³×C₄×C₉×C₄₃, …
maximal quotient of	C₂²×C₈×C₉×C₄₃, C₂×C₄²×C₉×C₄₃, C₂³×C₄×C₉×C₄₃, …
automorphism group of	C₃×C₁₉×C₁₇₃, C₄×C₂₇×C₁₇₃
outer automorphism group of	C₃×C₁₉×C₁₇₃, C₄×C₂₇×C₁₇₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.