Finite Group Databasebeta

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C₁₇×C₂₃×C₂₇ #72189145

order	10557
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₉×C₁₁×C₁₆ (order 6336) · Inn(G) = C₁ · Out(G) = C₂²×C₉×C₁₁×C₁₆
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₅₅₇
abelian	C₁₇×C₂₃×C₂₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₉	C₃×C₁₇×C₂₃
socle, prime radical	C₃×C₁₇×C₂₃	C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10557 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₀₅₅₇, C₂×D₁₀₅₅₇
maximal subgroup of	C₂×C₁₇×C₂₃×C₂₇, C₁₇×C₂₃×C₈₁, C₃×C₁₇×C₂₃×C₂₇, …
maximal normal subgroup of	C₂×C₁₇×C₂₃×C₂₇, C₁₇×C₂₃×C₈₁, C₃×C₁₇×C₂₃×C₂₇, …
maximal quotient of	C₂×C₁₇×C₂₃×C₂₇, C₁₇×C₂₃×C₈₁, C₃×C₁₇×C₂₃×C₂₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.