C₁₉×#10387 #18016346

order	4864
nilpotency class	3
isoclinism	isoclinic class of #10386
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#10387

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#393
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

414 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 90 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) = 51
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 3 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,26,28,31)(23,34)(27,43,35,39)(29,42,45,46)(32,49)(36,37)(41,44,48,51)(47,50);(21,27,28,35)(22,30)(26,39,31,43)(29,44,45,51)(32,47)(33,40)(41,46,48,42)(49,50);(20,21,25,29)(22,31,30,46)(23,35,37,51)(24,28,38,45)(26,40,42,33)(27,34,44,36)(32,41,47,39)(43,50,48,49)

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, 3375);