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D₄×C₁₉×#131 #18066104

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

Aliases

D₄×C₁₉×#131

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₉	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
socle	C₂²×C₁₉	C₂⁴×C₄
prime radical	D₄×#41×C₁₉	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₉ ◁ G

2814 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, 53133);