C₁₉×#13643 #18019602

order	4864
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#13643

Subgroups

	subgroup	G/H
center	C₈×C₁₉	#117
commutator	C₂×C₄	C₂²×C₈×C₁₉
Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
socle	C₂×C₁₉	#2163
prime radical	C₂³×C₁₉	M₃₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₉ ◁ C₁₉×#346 ◁ G

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

normal subgroups only

This group has 164 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) = 83
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 83 points:

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

Conjugacy classes & character table

1216 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6631);