Finite Group Databasebeta

← Prev (#72185040) Next (#72185042) →

C₂×C₃×C₈×C₁₂₁ #72185041

order	5808
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 3520
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

C₂×C₃×C₈×C₁₂₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₁₁	C₂²×C₃×C₁₁
socle, prime radical	C₂²×C₃×C₁₁	C₄×C₁₁
LCS	G ▷ C₁
UCS	C₁ ◁ G

66 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5808 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₁₆×C₁₂₁, C₃×C₄×C₈×C₁₂₁, C₂²×C₃×C₈×C₁₂₁, …
maximal normal subgroup of	C₂×C₃×C₁₆×C₁₂₁, C₃×C₄×C₈×C₁₂₁, C₂²×C₃×C₈×C₁₂₁, …
maximal quotient of	C₂×C₃×C₁₆×C₁₂₁, C₃×C₄×C₈×C₁₂₁, C₂²×C₃×C₈×C₁₂₁, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.