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C₂×C₃×C₄²×C₁₀₃ #72188586

order	9888
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 313344
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₄

Aliases

abelian	C₂×C₃×C₄²×C₁₀₃
multiplicative	(ℤ/18555)ˣ, (ℤ/19792)ˣ, (ℤ/24740)ˣ, (ℤ/37110)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂³×C₃×C₁₀₃
socle, prime radical	C₂³×C₃×C₁₀₃	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

216 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9888 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₄×C₈×C₁₀₃, C₃×C₄³×C₁₀₃, C₂²×C₃×C₄²×C₁₀₃, …
maximal normal subgroup of	C₂×C₃×C₄×C₈×C₁₀₃, C₃×C₄³×C₁₀₃, C₂²×C₃×C₄²×C₁₀₃, …
maximal quotient of	C₂×C₃×C₄×C₈×C₁₀₃, C₃×C₄³×C₁₀₃, C₂²×C₃×C₄²×C₁₀₃, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.