Finite Group Databasebeta

← Prev (#19150445) Next (#19150447) →

C₂×C₃²×C₃₁₁ #19150446

order	5598
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 14880
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃

Aliases

C₂×C₃²×C₃₁₁

Subgroups

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

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5598 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₂×C₃²×C₃₁₁⋊C₅
socle of	C₂×C₃²×C₃₁₁⋊C₅
maximal subgroup of	C₃²×C₄×C₃₁₁, C₃²×Dic₃₁₁, C₃×Dic₃×C₃₁₁, …
maximal normal subgroup of	C₃²×C₄×C₃₁₁, C₃²×Dic₃₁₁, C₃×Dic₃×C₃₁₁, …
maximal quotient of	C₃²×C₄×C₃₁₁, C₂²×C₃²×C₃₁₁, C₂×C₃²×C₅×C₃₁₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5598, 5);