Finite Group Databasebeta

← Prev (#72184391) Next (#72184393) →

C₂×C₃²×C₉×C₃₁ #72184392

order	5022
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 699840
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃³

Aliases

C₂×C₃²×C₉×C₃₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂×C₃³×C₃₁
socle, prime radical	C₂×C₃³×C₃₁	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

200 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5022 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃²×C₄×C₉×C₃₁, C₂²×C₃²×C₉×C₃₁, C₂×C₃²×C₂₇×C₃₁, …
maximal normal subgroup of	C₃²×C₄×C₉×C₃₁, C₂²×C₃²×C₉×C₃₁, C₂×C₃²×C₂₇×C₃₁, …
maximal quotient of	C₃²×C₄×C₉×C₃₁, C₂²×C₃²×C₉×C₃₁, C₂×C₃²×C₂₇×C₃₁, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.