Finite Group Databasebeta

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C₂×C₃×C₈×C₉×C₃₁ #72191663

order	13392
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 51840
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₃

Aliases

C₂×C₃×C₈×C₉×C₃₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄	C₂²×C₃²×C₃₁
socle, prime radical	C₂²×C₃²×C₃₁	C₃×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

220 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13392 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₉×C₁₆×C₃₁, C₃×C₄×C₈×C₉×C₃₁, C₂²×C₃×C₈×C₉×C₃₁
maximal normal subgroup of	C₂×C₃×C₉×C₁₆×C₃₁, C₃×C₄×C₈×C₉×C₃₁, C₂²×C₃×C₈×C₉×C₃₁
maximal quotient of	C₂×C₃×C₉×C₁₆×C₃₁, C₃×C₄×C₈×C₉×C₃₁, C₂²×C₃×C₈×C₉×C₃₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.