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C₇×C₉×C₃₂ #72181996

order	2016
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₃²×C₈ (order 576) · Inn(G) = C₁ · Out(G) = C₂³×C₃²×C₈
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₂₀₁₆
abelian	C₇×C₉×C₃₂
multiplicative	(ℤ/2017)ˣ, (ℤ/4034)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₁₆	C₂×C₃×C₇
socle, prime radical	C₂×C₃×C₇	C₃×C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2016 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇×C₉×C₆₄, C₂×C₇×C₉×C₃₂, C₇×C₂₇×C₃₂, …
maximal normal subgroup of	C₇×C₉×C₆₄, C₂×C₇×C₉×C₃₂, C₇×C₂₇×C₃₂, …
maximal quotient of	C₇×C₉×C₆₄, C₂×C₇×C₉×C₃₂, C₇×C₂₇×C₃₂, …
automorphism group of	C₂₀₁₇, C₂×C₂₀₁₇
outer automorphism group of	C₂₀₁₇, C₂×C₂₀₁₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.