C₁₉×#7439 #18013398

order	4864
nilpotency class	5
isoclinism	isoclinic class of #7396
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#7439

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#353
commutator	C₂×M₁₆	C₂×C₄×C₁₉
Frattini, cosocle	#408	C₂²×C₁₉
socle	C₂×C₁₉	#1352
prime radical	C₂×#41×C₁₉	D₄
LCS	G ▷ C₂×M₁₆ ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₁₉×#408 ◁ G

170 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 42 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)(20,21,24,29,26,30,42,57)(22,32,34,58,35,59,64,81)(23,28,38,51,39,53,68,55)(25,31,43,56,44,50,72,78)(27,45,46,37,48,65,74,66)(33,47,61,54,62,75,63,80)(36,49,41,70,60,76,71,83)(40,52,67,79,69,77,73,82);(20,22)(21,27)(23,37,39,66)(24,41,42,71)(25,36)(26,35)(28,49,53,76)(29,54,57,80)(30,48)(31,47)(32,52,59,77)(33,40,62,69)(34,43,64,72)(38,61)(44,60)(45,73)(46,56,74,78)(50,75)(51,58)(55,81)(63,68)(65,67)(70,79)(82,83)

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, 427);