Finite Group Databasebeta

← Prev (#22580233) Next (#22580235) →

C₂²×C₃²×C₁₃×C₁₉ #22580234

order	8892
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 62208
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₃

Aliases

abelian	C₂²×C₃²×C₁₃×C₁₉
multiplicative	(ℤ/10381)ˣ, (ℤ/13347)ˣ, (ℤ/20762)ˣ, (ℤ/26694)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8892 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃²×C₄×C₁₃×C₁₉, C₂³×C₃²×C₁₃×C₁₉, C₂²×C₃×C₉×C₁₃×C₁₉, …
maximal normal subgroup of	C₂×C₃²×C₄×C₁₃×C₁₉, C₂³×C₃²×C₁₃×C₁₉, C₂²×C₃×C₉×C₁₃×C₁₉, …
maximal quotient of	C₂×C₃²×C₄×C₁₃×C₁₉, C₂³×C₃²×C₁₃×C₁₉, C₂²×C₃×C₉×C₁₃×C₁₉, …
automorphism group of	C₇×C₁₄₈₃
outer automorphism group of	C₇×C₁₄₈₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8892, 137);