Finite Group Databasebeta

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C₂×C₁₃×C₁₇×C₂₇ #72190352

order	11934
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₃×C₄×C₉×C₁₆ (order 3456) · Inn(G) = C₁ · Out(G) = C₂×C₃×C₄×C₉×C₁₆
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₁₉₃₄
abelian	C₂×C₁₃×C₁₇×C₂₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₉	C₂×C₃×C₁₃×C₁₇
socle, prime radical	C₂×C₃×C₁₃×C₁₇	C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11934 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₁₉₃₄, D₂₃₈₆₈
maximal subgroup of	C₄×C₁₃×C₁₇×C₂₇, C₂²×C₁₃×C₁₇×C₂₇, C₂×D₅₉₆₇, …
maximal normal subgroup of	C₄×C₁₃×C₁₇×C₂₇, C₂²×C₁₃×C₁₇×C₂₇, C₂×D₅₉₆₇, …
maximal quotient of	C₄×C₁₃×C₁₇×C₂₇, C₂²×C₁₃×C₁₇×C₂₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.