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C₂×D₄×M₁₆×C₁₉ #18066097

order	4864
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁹

Aliases

C₂×D₄×M₁₆×C₁₉

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
socle	C₂³×C₁₉	C₂³×C₄
prime radical	C₂³×D₄×C₁₉	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

3218 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 53126);