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C₃×C₃₂×C₁₀₇ #72188919

order	10272
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₈×C₅₃ (order 3392) · Inn(G) = C₁ · Out(G) = C₂³×C₈×C₅₃
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₂₇₂
abelian	C₃×C₃₂×C₁₀₇
multiplicative	(ℤ/10273)ˣ, (ℤ/20546)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₆	C₂×C₃×C₁₀₇
socle, prime radical	C₂×C₃×C₁₀₇	C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10272 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₀₂₇₂, D₂₀₅₄₄
maximal subgroup of	C₃×C₆₄×C₁₀₇, C₂×C₃×C₃₂×C₁₀₇, C₉×C₃₂×C₁₀₇, …
maximal normal subgroup of	C₃×C₆₄×C₁₀₇, C₂×C₃×C₃₂×C₁₀₇, C₉×C₃₂×C₁₀₇, …
maximal quotient of	C₃×C₆₄×C₁₀₇, C₂×C₃×C₃₂×C₁₀₇, C₉×C₃₂×C₁₀₇, …
automorphism group of	C₁₀₂₇₃
outer automorphism group of	C₁₀₂₇₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.