C₁₉×#10084 #18016043

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

Aliases

direct product

C₁₉×#10084

Subgroups

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

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

normal subgroups only

This group has 484 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) = 55
transitive degree	μ_t(G) = 4864

A minimal faithful permutation representation — 3 generators on 55 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(24,25,30,35)(26,36,27,38)(28,34,29,33)(31,39,32,37)(40,41,45,43)(42,48,51,55)(44,52,54,47)(46,53,49,50);(20,21)(22,23)(24,26)(25,31)(27,30)(28,39)(29,37)(32,35)(33,38)(34,36)(40,42,45,51)(41,46,43,49)(44,53,54,50)(47,55,52,48);(21,23)(24,27,30,26)(25,32,35,31)(28,39,29,37)(33,38,34,36)(40,43,45,41)(42,49,51,46)(44,47,54,52)(48,53,55,50)

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, 3072);