C₁₉×#9932 #18015891

order	4864
nilpotency class	3
isoclinism	isoclinic class of #9930
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#9932

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₁₉×#3192	C₂
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

610 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 102 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) = 43
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 43 points:

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

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, 2920);