Finite Group Databasebeta

← Prev (#72189493) Next (#72189495) →

C₃²×C₄³×C₁₉ #72189494

order	10944
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 74317824
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃×C₄³

Aliases

abelian	C₃²×C₄³×C₁₉
multiplicative	(ℤ/14885)ˣ, (ℤ/29770)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂³	C₂³×C₃²×C₁₉
socle, prime radical	C₂³×C₃²×C₁₉	C₂³
LCS	G ▷ C₁
UCS	C₁ ◁ G

1548 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10944 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃²×C₄²×C₈×C₁₉, C₂×C₃²×C₄³×C₁₉
maximal normal subgroup of	C₃²×C₄²×C₈×C₁₉, C₂×C₃²×C₄³×C₁₉
maximal quotient of	C₃²×C₄²×C₈×C₁₉, C₂×C₃²×C₄³×C₁₉
automorphism group of	C₅×C₁₃×C₂₂₉
outer automorphism group of	C₅×C₁₃×C₂₂₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.