Finite Group Databasebeta

← Prev (#72192526) Next (#72192528) →

C₁₆×C₂₉×C₃₁ #72192527

order	14384
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃×C₄²×C₅×C₇ (order 6720) · Inn(G) = C₁ · Out(G) = C₂²×C₃×C₄²×C₅×C₇
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₄₃₈₄
abelian	C₁₆×C₂₉×C₃₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₂₉×C₃₁
socle, prime radical	C₂×C₂₉×C₃₁	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14384 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₄₃₈₄, D₂₈₇₆₈
Fitting subgroup of	D₁₄₃₈₄, Dic₇₁₉₂
maximal subgroup of	C₂₉×C₃₁×C₃₂, C₂×C₁₆×C₂₉×C₃₁, D₁₄₃₈₄, …
maximal normal subgroup of	C₂₉×C₃₁×C₃₂, C₂×C₁₆×C₂₉×C₃₁, D₁₄₃₈₄, …
maximal quotient of	C₂₉×C₃₁×C₃₂, C₂×C₁₆×C₂₉×C₃₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.