Finite Group Databasebeta

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C₁₆×C₂₃×C₂₉ #72189228

order	10672
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₄²×C₇×C₁₁ (order 4928) · Inn(G) = C₁ · Out(G) = C₂²×C₄²×C₇×C₁₁
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₆₇₂
abelian	C₁₆×C₂₃×C₂₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₂₃×C₂₉
socle, prime radical	C₂×C₂₃×C₂₉	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10672 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₀₆₇₂, D₂₁₃₄₄
maximal subgroup of	C₂₃×C₂₉×C₃₂, C₂×C₁₆×C₂₃×C₂₉, C₃×C₁₆×C₂₃×C₂₉, …
maximal normal subgroup of	C₂₃×C₂₉×C₃₂, C₂×C₁₆×C₂₃×C₂₉, C₃×C₁₆×C₂₃×C₂₉, …
maximal quotient of	C₂₃×C₂₉×C₃₂, C₂×C₁₆×C₂₃×C₂₉, C₃×C₁₆×C₂₃×C₂₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.