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C₂×C₂₇×C₁₆₉ #72187882

order	9126
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₃×C₄×C₉×C₁₃ (order 2808) · Inn(G) = C₁ · Out(G) = C₂×C₃×C₄×C₉×C₁₃
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₉₁₂₆
abelian	C₂×C₂₇×C₁₆₉
multiplicative	(ℤ/9127)ˣ, (ℤ/18254)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₉×C₁₃	C₂×C₃×C₁₃
socle, prime radical	C₂×C₃×C₁₃	C₉×C₁₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9126 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₉₁₂₆, D₁₈₂₅₂
maximal subgroup of	C₄×C₂₇×C₁₆₉, C₂²×C₂₇×C₁₆₉, C₂×C₈₁×C₁₆₉, …
maximal normal subgroup of	C₄×C₂₇×C₁₆₉, C₂²×C₂₇×C₁₆₉, C₂×C₈₁×C₁₆₉, …
maximal quotient of	C₄×C₂₇×C₁₆₉, C₂²×C₂₇×C₁₆₉, C₂×C₈₁×C₁₆₉, …
automorphism group of	C₉₁₂₇
outer automorphism group of	C₉₁₂₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.