Finite Group Databasebeta

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C₇×C₁₇×C₈₁ #72188356

order	9639
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃×C₁₆×C₂₇ (order 5184) · Inn(G) = C₁ · Out(G) = C₂²×C₃×C₁₆×C₂₇
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₉₆₃₉
abelian	C₇×C₁₇×C₈₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂₇	C₃×C₇×C₁₇
socle, prime radical	C₃×C₇×C₁₇	C₂₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9639 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₉₆₃₉, C₂×D₉₆₃₉
maximal subgroup of	C₂×C₇×C₁₇×C₈₁, C₇×C₁₇×C₂₄₃, C₃×C₇×C₁₇×C₈₁, …
maximal normal subgroup of	C₂×C₇×C₁₇×C₈₁, C₇×C₁₇×C₂₄₃, C₃×C₇×C₁₇×C₈₁, …
maximal quotient of	C₂×C₇×C₁₇×C₈₁, C₇×C₁₇×C₂₄₃, C₃×C₇×C₁₇×C₈₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.