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C₂×C₁₉×#2922 #18066078

order	4864
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁷×C₄

Aliases

C₂×C₁₉×#2922

Subgroups

	subgroup	G/H
center	C₂×C₄²×C₁₉	C₂³
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
socle	C₂³×C₁₉	C₂³×C₄
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₁₉ ◁ G

2222 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2128 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 53107);