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C₂²×C₄×C₂₃×C₃₁ #72189883

order	11408
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 126720
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂²×C₄×C₂₃×C₃₁
multiplicative	(ℤ/21405)ˣ, (ℤ/22832)ˣ, (ℤ/28540)ˣ, (ℤ/42810)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂³×C₂₃×C₃₁
socle, prime radical	C₂³×C₂₃×C₃₁	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

108 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11408 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₈×C₂₃×C₃₁, C₂×C₄²×C₂₃×C₃₁, C₂³×C₄×C₂₃×C₃₁
maximal normal subgroup of	C₂²×C₈×C₂₃×C₃₁, C₂×C₄²×C₂₃×C₃₁, C₂³×C₄×C₂₃×C₃₁
maximal quotient of	C₂²×C₈×C₂₃×C₃₁, C₂×C₄²×C₂₃×C₃₁, C₂³×C₄×C₂₃×C₃₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.