C₁₉×#10101 #18016060

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

Aliases

direct product

C₁₉×#10101

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

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

normal subgroups only

This group has 474 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)(22,30)(23,26)(24,28)(25,29)(27,31)(32,34)(33,35)(36,37,41,45)(38,46,39,43)(40,49,50,44)(42,48,51,47);(21,26)(23,24)(27,30)(28,29)(31,33)(34,35)(36,38,41,39)(37,42,45,51)(40,48,50,47)(43,49,46,44);(20,22,25,32)(21,27,29,35)(23,31,24,33)(26,34,28,30)(36,39,41,38)(37,43,45,46)(40,47,50,48)(42,44,51,49)

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, 3089);