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C₂³×C₃×C₁₉₁ #72184039

order	4584
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 63840
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂³×C₃×C₁₉₁
multiplicative	(ℤ/8043)ˣ, (ℤ/10724)ˣ, (ℤ/13788)ˣ, (ℤ/16086)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4584 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₃×C₄×C₁₉₁, C₂⁴×C₃×C₁₉₁, C₂³×C₉×C₁₉₁, …
maximal normal subgroup of	C₂²×C₃×C₄×C₁₉₁, C₂⁴×C₃×C₁₉₁, C₂³×C₉×C₁₉₁, …
maximal quotient of	C₂²×C₃×C₄×C₁₉₁, C₂⁴×C₃×C₁₉₁, C₂³×C₉×C₁₉₁, …
automorphism group of	C₃×C₇×C₃₈₃, C₄×C₇×C₃₈₃
outer automorphism group of	C₃×C₇×C₃₈₃, C₄×C₇×C₃₈₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.