Finite Group Databasebeta

← Prev (#72191028) Next (#72191030) →

C₂³×C₄²×C₉×C₁₁ #72191029

order	12672
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 3963617280
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁹×C₄

Aliases

abelian	C₂³×C₄²×C₉×C₁₁
multiplicative	(ℤ/34040)ˣ, (ℤ/34960)ˣ, (ℤ/40848)ˣ, (ℤ/47640)ˣ, (ℤ/47760)ˣ, (ℤ/49680)ˣ, (ℤ/51060)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₃	C₂⁵×C₃×C₁₁
socle, prime radical	C₂⁵×C₃×C₁₁	C₂²×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

9000 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12672 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₄×C₈×C₉×C₁₁, C₂²×C₄³×C₉×C₁₁, C₂⁴×C₄²×C₉×C₁₁
maximal normal subgroup of	C₂³×C₄×C₈×C₉×C₁₁, C₂²×C₄³×C₉×C₁₁, C₂⁴×C₄²×C₉×C₁₁
maximal quotient of	C₂³×C₄×C₈×C₉×C₁₁, C₂²×C₄³×C₉×C₁₁, C₂⁴×C₄²×C₉×C₁₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.