Finite Group Databasebeta

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C₃²×C₄×C₁₆×C₁₉ #72189484

order	10944
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 221184
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃×C₄

Aliases

C₃²×C₄×C₁₆×C₁₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₈	C₂²×C₃²×C₁₉
socle, prime radical	C₂²×C₃²×C₁₉	C₂×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

348 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10944 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃²×C₄×C₁₉×C₃₂, C₃²×C₈×C₁₆×C₁₉, C₂×C₃²×C₄×C₁₆×C₁₉
maximal normal subgroup of	C₃²×C₄×C₁₉×C₃₂, C₃²×C₈×C₁₆×C₁₉, C₂×C₃²×C₄×C₁₆×C₁₉
maximal quotient of	C₃²×C₄×C₁₉×C₃₂, C₃²×C₈×C₁₆×C₁₉, C₂×C₃²×C₄×C₁₆×C₁₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.