Finite Group Databasebeta

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C₁₆×C₁₇×C₅₃ #72192587

order	14416
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₄²×C₁₃×C₁₆ (order 6656) · Inn(G) = C₁ · Out(G) = C₂×C₄²×C₁₃×C₁₆
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₄₄₁₆
abelian	C₁₆×C₁₇×C₅₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₁₇×C₅₃
socle, prime radical	C₂×C₁₇×C₅₃	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14416 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₄₄₁₆, D₂₈₈₃₂
Fitting subgroup of	D₁₄₄₁₆, Dic₇₂₀₈
maximal subgroup of	C₁₇×C₃₂×C₅₃, C₂×C₁₆×C₁₇×C₅₃, D₁₄₄₁₆, …
maximal normal subgroup of	C₁₇×C₃₂×C₅₃, C₂×C₁₆×C₁₇×C₅₃, D₁₄₄₁₆, …
maximal quotient of	C₁₇×C₃₂×C₅₃, C₂×C₁₆×C₁₇×C₅₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.