C₁₉×#13813 #18019772

order	4864
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₁₉ · Schur multiplier (H₂) = C₂⁶×C₄

Aliases

direct product

C₁₉×#13813

Subgroups

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

2882 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 4 generators on 35 points:

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

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, 6801);

C19×#13813 #18019772

Aliases

Subgroups

Presentation

Conjugacy classes & character table

GAP

C₁₉×#13813 #18019772