C₁₉×#10628 #18016587

order	4864
nilpotency class	3
isoclinism	isoclinic class of #10370
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#10628

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	#124
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
socle	C₂²×C₁₉	#397
prime radical	C₂³×C₁₉	#123
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

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

normal subgroups only

This group has 292 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)(28,29)(30,38,41,51)(31,35)(32,36)(33,37)(34,40,48,45)(39,54,42,53)(43,49)(44,50)(46,52)(47,56,58,55)(57,59);(20,21,23,26)(22,24,27,25)(28,30)(29,34)(31,42)(32,45)(33,41)(35,47)(36,51)(37,48)(38,52)(39,44)(40,46)(43,55)(49,54)(50,58)(53,59)(56,57);(21,24)(22,27)(25,26)(28,31,32,43,33,44,46,57)(29,35,36,49,37,50,52,59)(30,39,40,55,41,42,45,56)(34,47,38,53,48,58,51,54)

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, 3616);