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C₂³×C₃²×C₄×C₅₃ #72193281

order	15264
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 53673984
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶×C₃

Aliases

abelian	C₂³×C₃²×C₄×C₅₃
multiplicative	(ℤ/29211)ˣ, (ℤ/33705)ˣ, (ℤ/38948)ˣ, (ℤ/50076)ˣ, (ℤ/58422)ˣ, (ℤ/67410)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂⁴×C₃²×C₅₃
socle, prime radical	C₂⁴×C₃²×C₅₃	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

1416 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	C₂³×C₃²×C₈×C₅₃, C₂²×C₃²×C₄²×C₅₃, C₂⁴×C₃²×C₄×C₅₃
maximal normal subgroup of	C₂³×C₃²×C₈×C₅₃, C₂²×C₃²×C₄²×C₅₃, C₂⁴×C₃²×C₄×C₅₃
maximal quotient of	C₂³×C₃²×C₈×C₅₃, C₂²×C₃²×C₄²×C₅₃, C₂⁴×C₃²×C₄×C₅₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.