Finite Group Databasebeta

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C₂×C₃×C₈×C₁₃×C₁₉ #72190296

order	11856
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 6912
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

C₂×C₃×C₈×C₁₃×C₁₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂²×C₃×C₁₃×C₁₉
socle, prime radical	C₂²×C₃×C₁₃×C₁₉	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11856 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₁₃×C₁₆×C₁₉, C₃×C₄×C₈×C₁₃×C₁₉, C₂²×C₃×C₈×C₁₃×C₁₉
maximal normal subgroup of	C₂×C₃×C₁₃×C₁₆×C₁₉, C₃×C₄×C₈×C₁₃×C₁₉, C₂²×C₃×C₈×C₁₃×C₁₉
maximal quotient of	C₂×C₃×C₁₃×C₁₆×C₁₉, C₃×C₄×C₈×C₁₃×C₁₉, C₂²×C₃×C₈×C₁₃×C₁₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.