Finite Group Databasebeta

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C₇×C₂₇×C₅₃ #72188692

order	10017
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃×C₄×C₉×C₁₃ (order 5616) · Inn(G) = C₁ · Out(G) = C₂²×C₃×C₄×C₉×C₁₃
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₀₁₇
abelian	C₇×C₂₇×C₅₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₉	C₃×C₇×C₅₃
socle, prime radical	C₃×C₇×C₅₃	C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10017 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₀₀₁₇, C₂×D₁₀₀₁₇
maximal subgroup of	C₂×C₇×C₂₇×C₅₃, C₇×C₅₃×C₈₁, C₃×C₇×C₂₇×C₅₃, …
maximal normal subgroup of	C₂×C₇×C₂₇×C₅₃, C₇×C₅₃×C₈₁, C₃×C₇×C₂₇×C₅₃, …
maximal quotient of	C₂×C₇×C₂₇×C₅₃, C₇×C₅₃×C₈₁, C₃×C₇×C₂₇×C₅₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.