C₁₉×#10086 #18016045

order	4864
nilpotency class	3
isoclinism	isoclinic class of #10078
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#10086

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂²×D₄×C₁₉	D₄
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

542 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 3 generators on 47 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(25,30)(26,31)(27,28)(32,33,37,35)(34,40,43,47)(36,44,46,39)(38,45,41,42);(20,21)(22,23)(24,25)(26,29)(27,31)(28,30)(32,34)(33,38)(35,41)(36,45)(37,43)(39,47)(40,44)(42,46);(21,23)(24,26,29,25)(27,31,28,30)(32,35,37,33)(34,41,43,38)(36,39,46,44)(40,45,47,42)

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 3074);