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C₃×C₃₂×C₁₃₁ #72190937

order	12576
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₅×C₈×C₁₃ (order 4160) · Inn(G) = C₁ · Out(G) = C₂³×C₅×C₈×C₁₃
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₂₅₇₆
abelian	C₃×C₃₂×C₁₃₁
multiplicative	(ℤ/12577)ˣ, (ℤ/25154)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₆	C₂×C₃×C₁₃₁
socle, prime radical	C₂×C₃×C₁₃₁	C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12576 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₂₅₇₆, D₂₅₁₅₂
maximal subgroup of	C₃×C₆₄×C₁₃₁, C₂×C₃×C₃₂×C₁₃₁, Dic₆₂₈₈, …
maximal normal subgroup of	C₃×C₆₄×C₁₃₁, C₂×C₃×C₃₂×C₁₃₁, Dic₆₂₈₈, …
maximal quotient of	C₃×C₆₄×C₁₃₁, C₂×C₃×C₃₂×C₁₃₁
automorphism group of	C₁₂₅₇₇
outer automorphism group of	C₁₂₅₇₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.