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C₉×C₁₆×C₂₉ #72183750

order	4176
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃×C₄²×C₇ (order 1344) · Inn(G) = C₁ · Out(G) = C₂²×C₃×C₄²×C₇
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₄₁₇₆
abelian	C₉×C₁₆×C₂₉
multiplicative	(ℤ/4177)ˣ, (ℤ/8354)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₈	C₂×C₃×C₂₉
socle, prime radical	C₂×C₃×C₂₉	C₃×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

30 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4176 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×C₂₉×C₃₂, C₂×C₉×C₁₆×C₂₉, C₁₆×C₂₇×C₂₉, …
maximal normal subgroup of	C₉×C₂₉×C₃₂, C₂×C₉×C₁₆×C₂₉, C₁₆×C₂₇×C₂₉, …
maximal quotient of	C₉×C₂₉×C₃₂, C₂×C₉×C₁₆×C₂₉, C₁₆×C₂₇×C₂₉, …
automorphism group of	C₄₁₇₇, C₂×C₄₁₇₇
outer automorphism group of	C₄₁₇₇, C₂×C₄₁₇₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.