C₁₉×#10613 #18016572

order	4864
nilpotency class	3
isoclinism	isoclinic class of #10611
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#10613

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#396
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂³×C₁₉	#126
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

276 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 2432

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

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, 3601);