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C₂×C₃×C₄×C₄₆₇ #72189702

order	11208
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 7456
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₃×C₄×C₄₆₇
multiplicative	(ℤ/14015)ˣ, (ℤ/28030)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂²×C₃×C₄₆₇
socle, prime radical	C₂²×C₃×C₄₆₇	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11208 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₄²×C₄₆₇, C₂×C₃×C₈×C₄₆₇, C₂²×C₃×C₄×C₄₆₇
maximal normal subgroup of	C₃×C₄²×C₄₆₇, C₂×C₃×C₈×C₄₆₇, C₂²×C₃×C₄×C₄₆₇
maximal quotient of	C₃×C₄²×C₄₆₇, C₂×C₃×C₈×C₄₆₇, C₂²×C₃×C₄×C₄₆₇
automorphism group of	C₅×C₂₈₀₃
outer automorphism group of	C₅×C₂₈₀₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.