C₁₉×#7423 #18013382

order	4864
nilpotency class	5
isoclinism	isoclinic class of #7422
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#7423

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1347
commutator	C₂×C₁₆	C₂×C₄×C₁₉
Frattini, cosocle	C₂×M₃₂	C₂²×C₁₉
prime radical	C₂³×C₁₉	D₁₆
LCS	G ▷ C₂×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ C₂×C₁₉×M₃₂ ◁ G

140 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 46 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)(22,33,35,64)(23,39,42,63)(24,46)(25,49)(26,52)(27,32)(28,34)(29,43,58,44)(30,41)(31,48)(36,69,37,70)(38,71,53,65)(40,60)(45,78,76,72)(47,81,50,57)(51,61)(54,79)(55,73)(56,68)(59,77,82,75)(62,67)(66,83)(74,80);(20,22,27,35)(21,28,32,56)(23,40,42,66)(24,47,25,50)(26,53,48,38)(29,57,58,81)(30,60,61,83)(31,62,52,55)(33,63,64,39)(34,43,68,44)(36,41,37,51)(45,79,76,74)(46,80,49,54)(59,70,82,69)(65,72,71,78)(67,77,73,75)

Conjugacy classes & character table

589 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 411);