Finite Group Databasebeta

← Prev (#72188643) Next (#72188645) →

C₂×C₃×C₈×C₁₃×C₁₆ #72188644

order	9984
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 786432
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₈

Aliases

abelian	C₂×C₃×C₈×C₁₃×C₁₆
multiplicative	(ℤ/15963)ˣ, (ℤ/20032)ˣ, (ℤ/21284)ˣ, (ℤ/31926)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₈	C₂³×C₃×C₁₃
socle, prime radical	C₂³×C₃×C₁₃	C₄×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

796 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9984 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₈×C₁₃×C₃₂, C₂×C₃×C₁₃×C₁₆², C₃×C₄×C₈×C₁₃×C₁₆, …
maximal normal subgroup of	C₂×C₃×C₈×C₁₃×C₃₂, C₂×C₃×C₁₃×C₁₆², C₃×C₄×C₈×C₁₃×C₁₆, …
maximal quotient of	C₂×C₃×C₈×C₁₃×C₃₂, C₂×C₃×C₁₃×C₁₆², C₃×C₄×C₈×C₁₃×C₁₆, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.