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C₃×C₃₂×C₁₀₁ #72188397

order	9696
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₄×C₈×C₂₅ (order 3200) · Inn(G) = C₁ · Out(G) = C₂²×C₄×C₈×C₂₅
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₉₆₉₆
abelian	C₃×C₃₂×C₁₀₁
multiplicative	(ℤ/9697)ˣ, (ℤ/19394)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₆	C₂×C₃×C₁₀₁
socle, prime radical	C₂×C₃×C₁₀₁	C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9696 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₉₆₉₆, D₁₉₃₉₂
maximal subgroup of	C₃×C₆₄×C₁₀₁, C₂×C₃×C₃₂×C₁₀₁, C₉×C₃₂×C₁₀₁, …
maximal normal subgroup of	C₃×C₆₄×C₁₀₁, C₂×C₃×C₃₂×C₁₀₁, C₉×C₃₂×C₁₀₁, …
maximal quotient of	C₃×C₆₄×C₁₀₁, C₂×C₃×C₃₂×C₁₀₁, C₉×C₃₂×C₁₀₁, …
automorphism group of	C₉₆₉₇
outer automorphism group of	C₉₆₉₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.