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C₂×C₃×C₄×C₄₆₁ #72189590

order	11064
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 7360
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₃×C₄×C₄₆₁
multiplicative	(ℤ/13835)ˣ, (ℤ/27670)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂²×C₃×C₄₆₁
socle, prime radical	C₂²×C₃×C₄₆₁	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11064 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₄²×C₄₆₁, C₂×C₃×C₈×C₄₆₁, C₂²×C₃×C₄×C₄₆₁
maximal normal subgroup of	C₃×C₄²×C₄₆₁, C₂×C₃×C₈×C₄₆₁, C₂²×C₃×C₄×C₄₆₁
maximal quotient of	C₃×C₄²×C₄₆₁, C₂×C₃×C₈×C₄₆₁, C₂²×C₃×C₄×C₄₆₁
automorphism group of	C₅×C₂₇₆₇
outer automorphism group of	C₅×C₂₇₆₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.