C₁₉×#13438 #18019397

order	4864
nilpotency class	4
isoclinism	isoclinic class of #13436
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#13438

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#2044
commutator, Frattini, cosocle	C₂×#41	C₂³×C₁₉
prime radical	C₂×#41×C₁₉	C₂³
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×#41×C₁₉ ◁ G

406 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 86 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)(20,21,27,32)(22,33,38,58)(23,39,44,72)(24,45,26,30)(25,47,49,31)(28,37,53,35)(29,54,57,42)(34,63,66,83)(36,68,48,62)(40,73,64,79)(41,71,43,70)(46,59,50,61)(51,74,80,81)(52,67,60,69)(55,78,82,65)(56,75,77,76);(20,22,27,38)(21,28,32,53)(23,40,44,64)(24,37,26,35)(25,48,49,36)(29,55,57,82)(30,58,45,33)(31,60,47,52)(34,41,66,43)(39,63,72,83)(42,74,54,81)(46,67,50,69)(51,77,80,56)(59,62,61,68)(65,75,78,76)(70,79,71,73);(20,23,24,41,27,44,26,43)(21,29,30,56,32,57,45,77)(22,34,35,64,38,66,37,40)(25,42,46,75,49,54,50,76)(28,51,33,55,53,80,58,82)(31,39,59,70,47,72,61,71)(36,65,67,81,48,78,69,74)(52,79,62,63,60,73,68,83)

Conjugacy classes & character table

532 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6426);