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C₂×C₂₇×C₁₉₇ #72189191

order	10638
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₄×C₉×C₄₉ (order 3528) · Inn(G) = C₁ · Out(G) = C₂×C₄×C₉×C₄₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₆₃₈
abelian	C₂×C₂₇×C₁₉₇
multiplicative	(ℤ/10639)ˣ, (ℤ/21278)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₉	C₂×C₃×C₁₉₇
socle, prime radical	C₂×C₃×C₁₉₇	C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10638 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₀₆₃₈, D₂₁₂₇₆
maximal subgroup of	C₄×C₂₇×C₁₉₇, C₂²×C₂₇×C₁₉₇, C₂×C₈₁×C₁₉₇, …
maximal normal subgroup of	C₄×C₂₇×C₁₉₇, C₂²×C₂₇×C₁₉₇, C₂×C₈₁×C₁₉₇, …
maximal quotient of	C₄×C₂₇×C₁₉₇, C₂²×C₂₇×C₁₉₇, C₂×C₈₁×C₁₉₇, …
automorphism group of	C₁₀₆₃₉
outer automorphism group of	C₁₀₆₃₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.