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C₂×C₄²×C₉×C₅₃ #72193278

order	15264
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 479232
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₄

Aliases

abelian	C₂×C₄²×C₉×C₅₃
multiplicative	(ℤ/19795)ˣ, (ℤ/39590)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₃	C₂³×C₃×C₅₃
socle, prime radical	C₂³×C₃×C₅₃	C₂²×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

324 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15264 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄×C₈×C₉×C₅₃, C₄³×C₉×C₅₃, C₂²×C₄²×C₉×C₅₃
maximal normal subgroup of	C₂×C₄×C₈×C₉×C₅₃, C₄³×C₉×C₅₃, C₂²×C₄²×C₉×C₅₃
maximal quotient of	C₂×C₄×C₈×C₉×C₅₃, C₄³×C₉×C₅₃, C₂²×C₄²×C₉×C₅₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.