C₁₉×#10428 #18016387

order	4864
nilpotency class	3
isoclinism	isoclinic class of #10078
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#10428

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

386 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 106 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)(21,22)(24,25)(26,30)(27,31)(28,32)(29,33)(34,37)(35,38)(36,39)(40,41,44,48)(42,45,50,55)(43,46,52,47)(49,53,51,54);(20,21)(22,23)(24,26,29,36)(25,30,33,39)(27,35,28,34)(31,38,32,37)(40,42,44,50)(41,45,48,55)(43,51,52,49)(46,54,47,53);(20,22,23,21)(25,31)(26,34)(27,28)(32,33)(35,36)(37,38)(41,46)(43,52)(45,53)(47,48)(49,51)(54,55)

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, 3416);