Finite Group Databasebeta

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C₃×C₅×C₁₆×C₄₇ #72189790

order	11280
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₄²×C₂₃ (order 2944) · Inn(G) = C₁ · Out(G) = C₂³×C₄²×C₂₃
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₁₂₈₀
abelian	C₃×C₅×C₁₆×C₄₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₃×C₅×C₄₇
socle, prime radical	C₂×C₃×C₅×C₄₇	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11280 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₁₂₈₀, D₂₂₅₆₀
maximal subgroup of	C₃×C₅×C₃₂×C₄₇, C₂×C₃×C₅×C₁₆×C₄₇, D₁₁₂₈₀, …
maximal normal subgroup of	C₃×C₅×C₃₂×C₄₇, C₂×C₃×C₅×C₁₆×C₄₇, D₁₁₂₈₀, …
maximal quotient of	C₃×C₅×C₃₂×C₄₇, C₂×C₃×C₅×C₁₆×C₄₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.