C₁₉×#13667 #18019626

order	4864
nilpotency class	5
isoclinism	isoclinic class of #13667
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#13667

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#2184
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ C₂×C₁₉×M₃₂ ◁ G

294 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 74 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) = 51
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 3 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,26)(22,30)(23,33)(24,36)(27,39)(28,42)(29,43)(31,35)(32,44)(34,49)(37,48)(38,40)(41,50)(45,46)(47,51);(20,21)(22,31)(23,35)(24,38)(25,27)(26,30)(28,33)(29,36)(32,47)(34,50)(37,51)(39,44)(40,49)(41,48)(42,45)(43,46);(22,32)(26,39)(30,44)(31,47)(34,45)(40,43)(42,50)(46,49)

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, 6655);