C₄×C₁₉×#328 #18014174

order	4864
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₄×C₁₉×#328

Subgroups

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

732 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);(6,10,11,19)(7,14)(12,20,13,15)(16,18);(5,6,8,12)(7,15,14,19)(9,13,17,11)(10,18,20,16)

Conjugacy classes & character table

1444 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 1203);

C4×C19×#328 #18014174

Aliases

Subgroups

Presentation

Conjugacy classes & character table

GAP

C₄×C₁₉×#328 #18014174