C₁₉×#10670 #18016629

order	4864
nilpotency class	3
isoclinism	isoclinic class of #10012
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#10670

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	#127
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
socle	C₂²×C₁₉	#399
prime radical	C₂³×C₁₉	#123
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

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

normal subgroups only

This group has 316 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) = 59
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 59 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,25,24,27,22,26)(28,29,34,39,33,38,32,37)(30,40,49,35,43,51,42,52)(31,44,48,54,47,36,46,55)(41,53,45,50,57,58,56,59);(21,25)(22,23)(26,27)(28,30,32,49,33,43,34,42)(29,35,37,51,38,52,39,40)(31,45,46,57,47,56,48,41)(36,53,54,50,44,58,55,59);(20,21,24,27)(22,25,23,26)(28,31,33,47)(29,36,38,44)(30,41,43,57)(32,46,34,48)(35,50,52,59)(37,54,39,55)(40,53,51,58)(42,56,49,45)

Conjugacy classes & character table

760 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 3658);