C₁₉×#13416 #18019375

order	4864
nilpotency class	4
isoclinism	isoclinic class of #13373
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#13416

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#486
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
socle	C₂×C₁₉	#2041
prime radical	C₁₉×#3150	C₂
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₁₉×#97 ◁ G

442 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 110 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)(22,25)(23,36)(24,43)(26,35)(27,32)(28,34)(29,39)(30,45)(31,44)(33,42)(37,46)(38,51)(40,49)(41,50)(47,48);(20,22)(21,28)(23,37)(24,31)(25,43)(26,30)(27,35)(29,41)(32,44)(33,40)(34,45)(36,39)(38,49)(42,48)(46,51)(47,50);(20,23,24,38,27,42,45,41)(21,29,30,48,32,49,43,37)(22,33,34,51,35,36,31,50)(25,46,44,40,26,47,28,39)

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6404);