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C₂²×C₈×C₉×C₅₃ #72193276

order	15264
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 119808
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂²×C₈×C₉×C₅₃
multiplicative	(ℤ/23433)ˣ, (ℤ/31244)ˣ, (ℤ/46866)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄	C₂³×C₃×C₅₃
socle, prime radical	C₂³×C₃×C₅₃	C₃×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

228 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	C₂²×C₉×C₁₆×C₅₃, C₂×C₄×C₈×C₉×C₅₃, C₂³×C₈×C₉×C₅₃
maximal normal subgroup of	C₂²×C₉×C₁₆×C₅₃, C₂×C₄×C₈×C₉×C₅₃, C₂³×C₈×C₉×C₅₃
maximal quotient of	C₂²×C₉×C₁₆×C₅₃, C₂×C₄×C₈×C₉×C₅₃, C₂³×C₈×C₉×C₅₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.