C₁₉×#13444 #18019403

order	4864
nilpotency class	4
isoclinism	isoclinic class of #13309
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#13444

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#469
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
socle	C₂×C₁₉	#2054
prime radical	C₁₉×#3414	C₂
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

392 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 106 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)(22,23)(24,37)(25,45)(26,47)(27,32)(28,33)(29,39)(30,44)(31,43)(34,49)(35,51)(36,41)(38,42)(40,48)(46,50);(20,22)(21,28)(23,37)(24,42)(25,29)(26,48)(27,36)(30,40)(31,38)(32,49)(33,44)(34,46)(35,43)(39,47)(41,45)(50,51);(20,23,24,38,43,51,46,49,27,41,25,39,26,40,44,28)(21,29,30,36,47,34,45,35,32,42,50,22,31,33,37,48)

Conjugacy classes & character table

760 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6432);