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C₂²×C₁₉×#410 #18066026

order	4864
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁹×C₄

Aliases

C₂²×C₁₉×#410

Subgroups

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

5278 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1672 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 53055);