C₄×C₁₉×H(3,ℤ/4) #18016656

order	4864
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₄³×C₁₉ · Schur multiplier (H₂) = C₂×C₄³

Aliases

direct product

C₄×C₁₉×H(3,ℤ/4)

Subgroups

	subgroup	G/H
center	C₄²×C₁₉	C₄²
commutator	C₄	C₄³×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
socle	C₂²×C₁₉	C₂×#95
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₄²×C₁₉ ◁ G

954 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 39 points:

(1,2,3,4)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39);(5,6)(7,13,15,19)(8,11)(9,12)(10,14,17,20)(16,18);(5,7)(6,10,12,17)(8,14)(9,15)(11,13,18,19)(16,20)

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, 3685);

C4×C19×H(3,ℤ/4) #18016656

Aliases

Subgroups

Presentation

Conjugacy classes & character table

GAP

C₄×C₁₉×H(3,ℤ/4) #18016656