Finite Group Databasebeta

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C₂×C₃×C₄×C₉×C₅₃ #72189901

order	11448
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 44928
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₃

Aliases

C₂×C₃×C₄×C₉×C₅₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂²×C₃²×C₅₃
socle, prime radical	C₂²×C₃²×C₅₃	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11448 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₈×C₉×C₅₃, C₃×C₄²×C₉×C₅₃, C₂²×C₃×C₄×C₉×C₅₃
maximal normal subgroup of	C₂×C₃×C₈×C₉×C₅₃, C₃×C₄²×C₉×C₅₃, C₂²×C₃×C₄×C₉×C₅₃
maximal quotient of	C₂×C₃×C₈×C₉×C₅₃, C₃×C₄²×C₉×C₅₃, C₂²×C₃×C₄×C₉×C₅₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.