Finite Group Databasebeta

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C₂×C₃×C₅³×C₁₃ #72188468

order	9750
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 35712000
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₅³

Aliases

C₂×C₃×C₅³×C₁₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

512 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9750 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₄×C₅³×C₁₃, C₂²×C₃×C₅³×C₁₃, C₂×C₅³×C₉×C₁₃, …
maximal normal subgroup of	C₃×C₄×C₅³×C₁₃, C₂²×C₃×C₅³×C₁₃, C₂×C₅³×C₉×C₁₃, …
maximal quotient of	C₃×C₄×C₅³×C₁₃, C₂²×C₃×C₅³×C₁₃, C₂×C₅³×C₉×C₁₃, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.