C₁₉×#12684 #18018643

order	4864
nilpotency class	3
isoclinism	isoclinic class of B(4,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₉×#12684

Subgroups

	subgroup	G/H
center	C₈×C₁₉	#120
commutator	C₂³	C₂²×C₈×C₁₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
socle	C₂×C₁₉	#1779
prime radical	C₁₉×#585	C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

894 conjugacy classes of subgroups; only the 210 normal subgroups are shown.

normal subgroups only

This group has 894 conjugacy classes of subgroups — too many to draw. Only its 210 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)(20,21,24,29,25,30,39,49,26,31,40,50,41,51,62,72)(22,27,34,44,35,45,58,68,33,43,56,66,57,67,77,81)(23,28,37,47,38,48,61,71,36,46,59,69,60,70,78,82)(32,52,54,73,55,74,76,83,53,42,63,64,75,65,79,80);(20,22)(21,27)(23,32)(24,34)(25,35)(26,33)(28,42)(29,44)(30,45)(31,43)(36,53)(37,54)(38,55)(39,58)(40,56)(41,57)(46,52)(47,64)(48,65)(49,68)(50,66)(51,67)(59,63)(60,75)(61,76)(62,77)(69,73)(70,74)(71,80)(72,81)(78,79)(82,83);(20,23)(21,28)(22,32)(24,37)(25,38)(26,36)(27,42)(29,47)(30,48)(31,46)(33,53)(34,54)(35,55)(39,61)(40,59)(41,60)(43,52)(44,64)(45,65)(49,71)(50,69)(51,70)(56,63)(57,75)(58,76)(62,78)(66,73)(67,74)(68,80)(72,82)(77,79)(81,83)

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, 5672);