Finite Group Databasebeta

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C₈×C₁₇×C₁₀₁ #72191935

order	13736
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₄×C₁₆×C₂₅ (order 6400) · Inn(G) = C₁ · Out(G) = C₂²×C₄×C₁₆×C₂₅
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₃₇₃₆
abelian	C₈×C₁₇×C₁₀₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₁₇×C₁₀₁
socle, prime radical	C₂×C₁₇×C₁₀₁	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13736 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₃₇₃₆, D₂₇₄₇₂
Fitting subgroup of	D₁₃₇₃₆, Dic₆₈₆₈
maximal subgroup of	C₁₆×C₁₇×C₁₀₁, C₂×C₈×C₁₇×C₁₀₁, D₁₃₇₃₆, …
maximal normal subgroup of	C₁₆×C₁₇×C₁₀₁, C₂×C₈×C₁₇×C₁₀₁, D₁₃₇₃₆, …
maximal quotient of	C₁₆×C₁₇×C₁₀₁, C₂×C₈×C₁₇×C₁₀₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.