Finite Group Databasebeta

← Prev (#72186250) Next (#72186252) →

C₈×C₂₉×C₃₁ #72186251

order	7192
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₃×C₄×C₅×C₇ (order 3360) · Inn(G) = C₁ · Out(G) = C₂³×C₃×C₄×C₅×C₇
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₇₁₉₂
abelian	C₈×C₂₉×C₃₁
multiplicative	(ℤ/7193)ˣ, (ℤ/14386)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₂₉×C₃₁
socle, prime radical	C₂×C₂₉×C₃₁	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7192 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₁₄₃₈₄, Dic₇₁₉₂
maximal subgroup of	C₁₆×C₂₉×C₃₁, C₂×C₈×C₂₉×C₃₁, C₃×C₈×C₂₉×C₃₁, …
maximal normal subgroup of	C₁₆×C₂₉×C₃₁, C₂×C₈×C₂₉×C₃₁, C₃×C₈×C₂₉×C₃₁, …
maximal quotient of	C₁₆×C₂₉×C₃₁, C₂×C₈×C₂₉×C₃₁, C₃×C₈×C₂₉×C₃₁
automorphism group of	C₇₁₉₃
outer automorphism group of	C₇₁₉₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.