C₁₉×#9389 #18015348

order	4864
nilpotency class	3
isoclinism	isoclinic class of #9385
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₉×#9389

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#392	C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

496 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 118 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)(20,21,25,30,26,28,45,46)(22,32,29,47,34,23,37,33)(24,40,42,49,27,31,44,35)(36,39,43,50,41,38,48,51);(20,22,33,40,27,36,51,28)(21,26,34,47,31,24,41,50)(23,30,42,37,38,35,45,48)(25,43,32,46,44,29,39,49);(21,28)(22,34)(23,38)(25,44)(29,48)(30,49)(31,40)(32,39)(35,46)(36,41)(37,43)(42,45)

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, 2377);