C₁₉×#10103 #18016062

order	4864
nilpotency class	3
isoclinism	isoclinic class of #10088
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#10103

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂³×C₁₉	#120
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

458 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 102 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) = 1216

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)(20,21,24,28)(22,26,30,35)(23,25,31,27)(29,34,32,33)(36,37,41,38)(39,46,47,51)(40,45,50,43)(42,49,44,48);(21,25)(23,31)(26,34)(27,28)(29,32)(33,35)(36,38,41,37)(39,44,47,42)(40,43,50,45)(46,49,51,48);(20,22,24,30)(21,26,28,35)(23,32,31,29)(25,33,27,34)(36,39)(37,42)(38,44)(40,49)(41,47)(43,51)(45,46)(48,50)

Conjugacy classes & character table

589 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 3091);