C₁₉×#7337 #18013296

order	4864
nilpotency class	4
isoclinism	isoclinic class of #353
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#7337

Subgroups

	subgroup	G/H
center	C₈×C₁₉	#99
commutator	C₂×C₄	C₂×C₁₆×C₁₉
Frattini, cosocle	C₂×M₃₂	C₂²×C₁₉
socle	C₂×C₁₉	#1314
prime radical	C₂×#41×C₁₉	C₈
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₉ ◁ C₂×C₈×C₁₉ ◁ C₂×C₁₉×M₃₂ ◁ G

154 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 54 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) = 83
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 2 generators on 83 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,30,25,32,44,57,26,29,43,53,46,54,70,77,27,31,45,56,47,58,71,79,23,38,40,55,41,65,67,78)(22,33,35,59,36,60,63,80,34,28,48,49,61,51,72,74,37,52,42,68,64,76,69,82,39,50,62,73,66,75,81,83);(20,22)(21,28)(23,39)(24,42)(25,36)(26,34)(27,37)(29,52)(30,49)(31,50)(32,51)(33,38)(35,45)(40,48)(41,66)(43,62)(44,69)(46,61)(47,64)(53,68)(54,76)(55,59)(56,73)(57,74)(58,75)(60,65)(63,71)(67,72)(70,81)(77,82)(78,80)(79,83)

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 325);