C₁₉×#7832 #18013791

order	4864
nilpotency class	3
isoclinism	isoclinic class of #7734
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#7832

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
LCS	G ▷ C₂×C₄² ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

322 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 94 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) = 67
transitive degree	μ_t(G) = 4864

A minimal faithful permutation representation — 3 generators on 67 points:

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

Conjugacy classes & character table

703 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 820);