Finite Group Databasebeta

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C₅×C₁₆×C₁₉₁ #72193287

order	15280
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₄²×C₅×C₁₉ (order 6080) · Inn(G) = C₁ · Out(G) = C₂²×C₄²×C₅×C₁₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₅₂₈₀
abelian	C₅×C₁₆×C₁₉₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₅×C₁₉₁
socle, prime radical	C₂×C₅×C₁₉₁	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15280 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₅₂₈₀, D₃₀₅₆₀
Fitting subgroup of	D₁₅₂₈₀, Dic₇₆₄₀
maximal subgroup of	C₅×C₃₂×C₁₉₁, C₂×C₅×C₁₆×C₁₉₁, D₁₅₂₈₀, …
maximal normal subgroup of	C₅×C₃₂×C₁₉₁, C₂×C₅×C₁₆×C₁₉₁, D₁₅₂₈₀, …
maximal quotient of	C₅×C₃₂×C₁₉₁, C₂×C₅×C₁₆×C₁₉₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.