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C₂×C₃²×C₄²×C₅₃ #72193279

order	15264
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 3833856
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₃×C₄

Aliases

C₂×C₃²×C₄²×C₅₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂³×C₃²×C₅₃
socle, prime radical	C₂³×C₃²×C₅₃	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

648 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×C₃²×C₄×C₈×C₅₃, C₃²×C₄³×C₅₃, C₂²×C₃²×C₄²×C₅₃
maximal normal subgroup of	C₂×C₃²×C₄×C₈×C₅₃, C₃²×C₄³×C₅₃, C₂²×C₃²×C₄²×C₅₃
maximal quotient of	C₂×C₃²×C₄×C₈×C₅₃, C₃²×C₄³×C₅₃, C₂²×C₃²×C₄²×C₅₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.