Finite Group Databasebeta

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C₃×C₈×C₆₇₃ #72194124

order	16152
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₃×C₇×C₃₂ (order 5376) · Inn(G) = C₁ · Out(G) = C₂³×C₃×C₇×C₃₂
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₆₁₅₂
abelian	C₃×C₈×C₆₇₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₃×C₆₇₃
socle, prime radical	C₂×C₃×C₆₇₃	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

16152 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₆₁₅₂, D₃₂₃₀₄
Fitting subgroup of	Dic₈₀₇₆, D₁₆₁₅₂
maximal subgroup of	C₃×C₁₆×C₆₇₃, C₂×C₃×C₈×C₆₇₃, Dic₈₀₇₆, …
maximal normal subgroup of	C₃×C₁₆×C₆₇₃, C₂×C₃×C₈×C₆₇₃, Dic₈₀₇₆, …
maximal quotient of	C₃×C₁₆×C₆₇₃, C₂×C₃×C₈×C₆₇₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.