Finite Group Databasebeta

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C₃×C₆₄×C₇₃ #72192202

order	14016
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₈×C₉×C₁₆ (order 4608) · Inn(G) = C₁ · Out(G) = C₂²×C₈×C₉×C₁₆
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₄₀₁₆
abelian	C₃×C₆₄×C₇₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃₂	C₂×C₃×C₇₃
socle, prime radical	C₂×C₃×C₇₃	C₃₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

28 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14016 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₄₀₁₆, D₂₈₀₃₂
Fitting subgroup of	D₁₄₀₁₆, Dic₇₀₀₈
maximal subgroup of	C₃×C₇₃×C₁₂₈, C₂×C₃×C₆₄×C₇₃, D₁₄₀₁₆, …
maximal normal subgroup of	C₃×C₇₃×C₁₂₈, C₂×C₃×C₆₄×C₇₃, D₁₄₀₁₆, …
maximal quotient of	C₃×C₇₃×C₁₂₈, C₂×C₃×C₆₄×C₇₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.