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C₃×C₅²×C₈×C₁₆ #72188307

order	9600
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1966080
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₅×C₈

Aliases

abelian	C₃×C₅²×C₈×C₁₆
multiplicative	(ℤ/9881)ˣ, (ℤ/19762)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₈	C₂²×C₃×C₅²
socle, prime radical	C₂²×C₃×C₅²	C₄×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

832 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9600 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₅²×C₈×C₃₂, C₃×C₅²×C₁₆², C₂×C₃×C₅²×C₈×C₁₆, …
maximal normal subgroup of	C₃×C₅²×C₈×C₃₂, C₃×C₅²×C₁₆², C₂×C₃×C₅²×C₈×C₁₆, …
maximal quotient of	C₃×C₅²×C₈×C₃₂, C₃×C₅²×C₁₆², C₂×C₃×C₅²×C₈×C₁₆, …
automorphism group of	C₄₁×C₂₄₁
outer automorphism group of	C₄₁×C₂₄₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.