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C₃⁴×C₈×C₁₉ #72190708

order	12312
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1746800640
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃⁶

Aliases

C₃⁴×C₈×C₁₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₃⁴×C₁₉
socle, prime radical	C₂×C₃⁴×C₁₉	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

1696 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12312 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃⁴×C₁₆×C₁₉, C₂×C₃⁴×C₈×C₁₉
maximal normal subgroup of	C₃⁴×C₁₆×C₁₉, C₂×C₃⁴×C₈×C₁₉
maximal quotient of	C₃⁴×C₁₆×C₁₉, C₂×C₃⁴×C₈×C₁₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.