C₁₉×#10665 #18016624

order	4864
nilpotency class	3
isoclinism	isoclinic class of #10012
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#10665

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	#127
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
socle	C₂²×C₁₉	#399
prime radical	C₁₉×#532	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

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

normal subgroups only

This group has 334 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) = 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)(20,21,22,25,24,27,23,26)(28,29,32,37,33,38,34,48)(30,39,41,51,43,55,42,35)(31,44,46,54,47,36,49,53)(40,56,45,59,57,52,58,50);(20,21)(22,26)(23,25)(24,27)(28,30,34,41,33,43,32,42)(29,35,48,39,38,51,37,55)(31,45,49,57,47,58,46,40)(36,52,54,50,44,56,53,59);(21,25)(22,23)(26,27)(28,31)(29,36)(30,40)(32,46)(33,47)(34,49)(35,50)(37,53)(38,44)(39,56)(41,45)(42,58)(43,57)(48,54)(51,59)(52,55)

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, 3653);