Finite Group Databasebeta

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C₅×C₇×C₁₆×C₁₇ #72188258

order	9520
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃×C₄²×C₁₆ (order 3072) · Inn(G) = C₁ · Out(G) = C₂²×C₃×C₄²×C₁₆
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₉₅₂₀
abelian	C₅×C₇×C₁₆×C₁₇
multiplicative	(ℤ/9521)ˣ, (ℤ/19042)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₅×C₇×C₁₇
socle, prime radical	C₂×C₅×C₇×C₁₇	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9520 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₉₅₂₀, D₁₉₀₄₀
maximal subgroup of	C₅×C₇×C₁₇×C₃₂, C₂×C₅×C₇×C₁₆×C₁₇, C₃×C₅×C₇×C₁₆×C₁₇, …
maximal normal subgroup of	C₅×C₇×C₁₇×C₃₂, C₂×C₅×C₇×C₁₆×C₁₇, C₃×C₅×C₇×C₁₆×C₁₇, …
maximal quotient of	C₅×C₇×C₁₇×C₃₂, C₂×C₅×C₇×C₁₆×C₁₇, C₃×C₅×C₇×C₁₆×C₁₇
automorphism group of	C₉₅₂₁
outer automorphism group of	C₉₅₂₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.